Dissertations / Theses: 'Correlation functions'

1

Nirschl, Michael. "Superconformal symmetry and correlation functions." Thesis, University of Cambridge, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.615123.

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Peláez, Arzúa Monica Marcela. "Infrared correlation functions in Quantum Chromodynamics." Thesis, Paris 6, 2015. http://www.theses.fr/2015PA066491/document.

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Le but de cette thèse est l'étude des fonctions de corrélation des théries Yang-Mills dans le régime infrarouge. Il est connu que, à cause de l'invariance jauge, il est nécessaire de fixer la jauge pour calculer des valeurs moyennes analytiquement. La procedure de fixation gauge standard est la procedure de Faddeev-Popov (FP). Le Lagrangien de FP permet de faire des calculs perturbatifs pour la Chromodynamique Quantique dans le régime de hautes énergies dont les résultats sont comparés avec succès avec des expériences. Cependant, dans le régime de basses énergies, il se trouve que la constante de couplage, calculée avec la procedure antérieure, diverge. En conséquence, la théorie des perturbations standard n'est plus valide. D'autre part, les simulations du réseau trouvent que la constante de couplage est finie avec une valeur modérée même dans le régime infrarouge. Ceci suggère qu'il devrait exister une manière de faire des calculs perturbatifs également dans le régime infrarouge. Cette différence dans la constante de couplage peut être due au fait que la procedure de FP n'est pas bien justifiée dans ce régime. Nous proposons de modifier le Lagrangien de FP avec un terme massif pour les gluons. Cette modification est également justifiée par le fait que le réseau trouve un propagateur du gluon qui paraît massive aux basses énergies. Nous utilisons cette version massive pour calculer à une boucle les fonctions de corrélations à deux et trois points pour une configuration cinématique générale et en dimension quelconque dans la jauge de Landau. On trouve que les comparaisons de notre calcul à une boucle avec les résultat du réseau donnent, en géneral, un très bon accord
The aim of this thesis is to investigate the infrared behaviour of Yang-Mills correlation functions. It is known that the gauge invariance of the theory brings as a consequence the necessity of a gauge fixing procedure in order to compute expectation values analytically. The standard procedure for fixing the gauge is the Faddeev-Popov (FP) procedure which allows one to do perturbation theory in the ultraviolet regime. Perturbative calculations using the FP gauge fixed action successfully reproduce Quantum Chromodynamics observables measured by experiments in the ultraviolet regime. In the infrared regime the coupling constant of the theory computed with the above procedure diverges, and standard perturbation theory does not seem to be valid. However, lattice simulations show that the coupling constant takes finite and not very large value. This suggests that some kind of perturbative calculations should be valid even in the infrared regime. The theoretical justification for the FP procedure depends on the absence of Gribov copies and hence is not valid in the infrared regime (where such copies exist). To correct this we propose to add a mass term for the gluons in the gauge-fixed Lagrangian. The gluon mass term is also motivated by lattice simulations which observe that the gluon propagator behaves as it was massive in the infrared regime. We use this massive extension of the FP gauge fixed action to compute the one loop correction of the two- and three-point correlation functions in the Landau gauge for arbitrary kinematics and dimension. Our one-loop calculations are enough, in general, to reproduce with good accuracy the lattice data available in the literature

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3

Parry, Andrew Owen. "Correlation functions at continuous wetting transitions." Thesis, University of Bristol, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.330318.

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4

Ding, You. "Spinfoams : simplicity constraints ans correlation functions." Thesis, Aix-Marseille 2, 2011. http://www.theses.fr/2011AIX22074/document.

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Dans cette thèse, nous étudions l’implémentation des contraintes de simplicité dans le nouveau modèle de mousses de spin d’Engle-Pereira-Rovelli-Livine, ainsi que les fonctions de corrélation à deux points de ce modèle. Nous définissons d’une manière simple l’espace de Hilbert limite de la théorie, puis montrons directement que toutes les contraintes s’annulent faiblement sur cet espace. Nous observons que la solution générale a cette contrainte (imposée faiblement) dépend d’un nombre quantique, en plus de ceux de la gravitation quantique a boucles. Nous généralisons également cette construction pour la version de Kaminski-Kisielowski-Lewandowski, ou la mousse n’est pas duale à une triangulation. Nous montrons que cette théorie peut aussi être obtenue comme une théorie BF satisfaisant la contrainte de simplicité, cette fois discrétisée sur un 2-complexe cellulaire oriente. Enfin, nous calculons la fonction de corrélation a deux points du modèle de mousses de spin Engle-Pereira-Rovelli-Livine avec la signature lorentzienne, et nous montrons que la fonction a deux points que nous obtenons correspond dans une certaine limite a celle obtenue a partir du calcul de Regge lorentzien
In this thesis we study the implementation of simplicity constraints that defines the recent Engle-Pereira-Rovelli-Livine spinfoam model and two-point correlation functions of this model. We define in a simple way the boundary Hilbert space of the theory; then show directly that all constraints vanish on this space in a weak sense. We point out that the general solution to this constraint (imposed weakly) depends on a quantum number in addition to those of loop quantum gravity. We also generalize this construction to Kami´nski-Kisielowski-Lewandowski version where the foam is not dual to a triangulation. We show that this theory can still be obtained as a constrained BF theory satisfying the simplicity constraint, now discretized on a general oriented 2-cell complex. Finally, we calculate the twopoint correlation function of the Engle-Pereira-Rovelli-Livine spinfoam model in the Lorentzian signature, and show the two-point function we obtain exactly matches the one obtained from Lorentzian Regge calculus in some limit

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Hotchkiss, Alastair Jeremy. "Generalised cross correlation functions for physical applications." Thesis, University of Exeter, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.262492.

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Matusis, Alec (Alec L. ). 1971. "CFT correlation functions from AdS/CFT correspondence." Thesis, Massachusetts Institute of Technology, 1999. http://hdl.handle.net/1721.1/85332.

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Vachaspati, Pranjal. "Optimizing tensor contractions for nuclear correlation functions." Thesis, Massachusetts Institute of Technology, 2014. http://hdl.handle.net/1721.1/92687.

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Thesis: S.B., Massachusetts Institute of Technology, Department of Physics, 2014.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 37-38).
Nuclear correlation functions reveal interesting physical properties of atomic nuclei, including ground state energies and scattering potentials. However, calculating their values is computationally intensive due to the fact that the number of terms from quantum chromodynamics in a nuclear wave function scales exponentially with atomic number. In this thesis, we demonstrate two methods for speeding up this computation. First, we represent a correlation function as a sum of the determinants of many small matrices, and exploit similarities between the matrices to speed up the calculations of the determinants. We also investigate representing a correlation function as a sum of functions of bipartite graphs, and use isomorph-free exhaustive generation techniques to find a minimal set of graphs that represents the computation.
by Pranjal Vachaspati.
S.B.

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Zhong, Deliang. "Correlation Functions in Integrable Higher Dimensional CFTs." Thesis, Sorbonne université, 2019. http://www.theses.fr/2019SORUS433.

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Dans cette thèse, nous étudions les fonctions de corrélation à deux points ou plus de la théorie N = 4 super Yang-Mills (SYM) et ses déformations. On pense que cette théorie et ses déformations sont intégrables dans la limite planaire pour toutes les valeurs de la constante de couplage, ce qui nous permet de calculer plus efficacement diverses grandeurs physiques. Nous commençons par passer en revue les bases de la théorie N = 4 SYM et les outils d’intégrabilité nécessaires. Dans la partie II, nous présentons le formalisme en hexagone pour le calcul des constantes de structure de la théorie N = 4 SYM. En utilisant l’ansatz de Bethe imbriqué, nous étudions la constante de structure de deux opérateurs BPS et d’un opérateur non BPS du sous-secteur su (1, 1 | 2) dans les limites de couplage faible et forte. Le résultat de couplage faible est appliqué à l’étude du développement en ondes partielles conformes des fonctions asymptotiques à quatre points. A fort couplage, le résultat est appliqué pour le calcul des constantes de structure Heavy-Heavy-Light. Dans la partie III, nous nous concentrons sur une limite de double échelle particulière de la théorie N = 4 SYM, la limite de fishnet. Le lagrangien est obtenu à partir du processus de déformation et nous en présentons les théorèmes de non-renormalisation. En outre, nous donnons la première preuve de la symétrie du Yangien pour une grande classe de diagrammes de fishnet, en utilisant la fameuse relation RTT de l’intégrabilité. En utilisant les techniques d'intégrabilité héritées de la théorie N = 4 SYM, nous trouvons également que la limite du continuum des diagrammes de Feynman en fishnet peut être décrit comme un modèle sigma AdS
In this thesis, we study two- and higher-point correlation functions of the N = 4 super Yang-Mills theory (SYM) and its deformations. This theory and its deformations are believed to be integrable in the planar limit for any values of the coupling constant, which allow us to compute various physical quantities more efficiently. The basics of N = 4 SYM and the necessary integrability tools are reviewed in the very beginning. In part II, we review the hexagon formalism for computing structure constant in N = 4 SYM. Using the nested Bethe ansatz techniques, we investigate the structure constant of two BPS operators and one non-BPS operator in the su(1, 1|2) subsector in both weak and strong coupling limit. The weak coupling result is applied to the study of the conformal partial wave expansion of asymptotic four-point functions. At strong coupling, the result is applied to the Heavy-Heavy-Light structure constants. In part III, we focus on a particular double scaling limit of N = 4 SYM, namely the fishnet limit. The Lagrangian is obtained from the deformation process, and we present the non-renormalization theorems about it. Besides, we give the first principle proof of the Yangian symmetry for a large class of fishnet Feynman diagrams, using the famous RTT-formulation of integrability. Using the integrability techniques inherited from N = 4 SYM, we also find that the continuum limit of fishnet Feynman diagrams admit an AdS sigma model description

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9

Schäfer, Rudi. "Correlation functions and fidelity decay in chaotic systems." [S.l. : s.n.], 2004. http://archiv.ub.uni-marburg.de/diss/z2004/0660/.

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10

Wilking, Philipp [Verfasser]. "Statistical properties of cosmological correlation functions / Philipp Wilking." Bonn : Universitäts- und Landesbibliothek Bonn, 2015. http://d-nb.info/1077289766/34.

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11

Kobayashi, Miki U. "Determination of dynamical correlation functions in chaotic systems." 京都大学 (Kyoto University), 2008. http://hdl.handle.net/2433/136009.

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Sikorowski, Jakub. "Correlation functions in maximally supersymmetric Yang-Mills theory." Thesis, University of Oxford, 2015. https://ora.ox.ac.uk/objects/uuid:1257e3bc-5f1d-4896-8859-a5544ce8ac97.

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In this thesis we consider the planar maximally supersymmetric Yang-Mills theory. First, we look at the correlation function of a null Wilson loop with four edges and a local operator at weak coupling. We use the Lagrangian insertion technique to find the integral representation up to two loops. Performing the integrals with a method closely linked to the dual space formalism for the scattering amplitudes, we explicitly compute the two loop result. We demonstrate the connection between the calculated observable and the cusp anomalous dimension by recovering the three loop value of the cusp anomalous dimension. We also explore the advantages of expressing the loop integrand in twistor variables. The second observable we look at is the four point correlation function of the BMN operators on a line at strong coupling. In order to access this regime we perform a semi-classical computation in the classical string theory. Considering area of an extended minimal surface stretched between the four operators, we find two different saddle points. We show that the extended minimal surface is sub-dominant to the saddle point composed of three geodesic strings joining the four operators in a sequence. The result is that, to the leading order at strong coupling, the considered correlation function is equal to its tree-level value when all operators are on a line.

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13

Chen, Kan. "Zero-frequency response functions and correlation functions in the Kondo and Anderson models /." The Ohio State University, 1988. http://rave.ohiolink.edu/etdc/view?acc_num=osu148759630735854.

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14

Tomberg, Alexandre. "Renormalisation group and critical correlation functions in dimension four." Thesis, University of British Columbia, 2015. http://hdl.handle.net/2429/54301.

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Critical phenomena and phase transitions are important subjects in statistical mechanics and probability theory. They are connected to the phenomenon of universality that makes the study of mathematically simple models physically relevant. Examples of such models include ferromagnetic spin systems such as the Ising, O(n) and n-component |φ|⁴ models, but also the self-avoiding walk that has been observed to formally correspond to a "zero-component" spin model by de Gennes. Our subject in this thesis is the extension and application of a rigorous renormalisation group method developed by Bauerschmidt, Brydges and Slade to study the critical behaviour of the continuous-time weakly self-avoiding walk and of the n-component |φ|⁴ model on the 4-dimensional square lattice ℤ⁴. Although a "zero-component" vector is mathematically undefined (at least naively), we are able to interpret the weakly self-avoiding walk in a mathematically rigorous manner as the n = 0 case of the n-component |φ|⁴ model, and provide a unified treatment of both models. For the |φ|⁴ model, we determine the asymptotic decay of the critical correlation functions including the logarithmic corrections to Gaussian scaling, for n ≥ 1. This extends previously known results for n = 1 to all n ≥ 1, and also observes new phenomena for n > 1, all with a new method of proof. For the continuous-time weakly self-avoiding walk, we determine the decay of the critical generating function for the "watermelon" network consisting of p weakly mutually- and self-avoiding walks, for all p ≥ 1, including the logarithmic corrections. This extends a previously known result for p = 1, for which there is no logarithmic correction, to a much more general setting.
Science, Faculty of
Mathematics, Department of
Graduate

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15

Alavi, Saman. "Density corrections to transport coefficients from time correlation functions." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape7/PQDD_0019/NQ46308.pdf.

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Macdonald, Evan David. "Correlation functions in thin films : identities, invariances and algebras." Thesis, Imperial College London, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.392437.

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Boulter, Christopher John. "Effective Hamiltonian models and correlation functions at wetting transitions." Thesis, Imperial College London, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.307449.

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Silk, James Brian. "Evaluation of correlation functions in integrable quantum field theories." Thesis, Durham University, 2012. http://etheses.dur.ac.uk/4447/.

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The aim of this thesis is to explore correlation functions in two dimensional quantum field theories in two distinct ways. In part I a new method for calculating the differential equations parametrising the correlation functions of twist fields associated with the U (1) symmetry of the Dirac model is presented. While developing this method a new family of descendent twist fields are identified and their form factors calculated. This provides a novel way of calculating the vacuum expectation values of the primary twist fields and is shown to be entirely consistent with known results. The method of calculating the correlation functions of twist fields provides a parametrisation of several other correlation functions for various quantum states. Since this method relies on the Ward identities found in a double copy model it is hoped to have wider applications in other free fermion models. Part II concerns the truncated conformal space approach which has been developed to approximate perturbed conformal field theories. In this part the theory underpinning the approach is discussed and a working algorithm is developed for both bulk and boundary perturbed minimal models. The energy levels, mass gaps and one point functions of various models are computed using the truncated conformal space approach and are shown to be in good agreement with previous calculations. A possible method for using this approach to approximate two point functions in perturbed conformal field theories is discussed.

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Artiles, Oswaldo. "Multinucleon Short-range Correlation Model for Nuclear Spectral Functions." FIU Digital Commons, 2017. http://digitalcommons.fiu.edu/etd/3384.

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The main goal of the research presented in my dissertation was to develop a theoretical model for relativistic nuclear spectral functions at high missing momenta and removal energies based on the multi-nucleon short-range correlation (SRC) model. The nuclear spectral functions are necessary for the description of high energy nuclear processes currently being studied at different labs such as JLAB, LHC and FNAL. The model followed the effective Feynman diagrammatic approach in order to ac-count for the relativistic effects important in the SRC domain. In addition to the two-nucleon (2N) SRC with center of mass motion contribution, the contribution of the three-nucleon SRCs to the spectral functions was also derived. The latter was modeled based on the assumption that the 3N SRCs are a product of two sequential short range nucleon-nucleon (NN) interactions. The nuclear spectral functions models were derived from two theoretical frameworks for evaluating covariant Feynman diagrams: In the first, referred to as the virtual nucleon approximation, the Feynman diagrams were reduced to the time ordered non-covariant diagrams by evaluating the nucleon spectators in the SRC at their positive energy poles, neglecting explicitly the contribution from vacuum diagrams. In the second approach, referred to as the light-front approximation, the boost invariant nuclear spectral function was formulated in the light-front reference frame in which case the vacuum diagrams are kinematically suppressed and the bound nucleon is described by its light-front variables such as momentum fraction, transverse momentum and invariant mass. On the basis of the derived nuclear spectral functions, the corresponding computational models were developed from which the numerical estimates of the SRC spectral functions, the SRC momentum distributions, and the SRC density matrices were obtained.

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Doobary, Reza Colin. "Correlation functions, scattering amplitudes and the superconformal partial wave." Thesis, Durham University, 2016. http://etheses.dur.ac.uk/11562/.

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In this thesis we explore aspects of correlation functions and scattering amplitudes in supersymmetric field theories. Firstly, we study correlation functions and scattering amplitudes in the perturbative regime of N=4 supersymmetric Yang-Mills theory. Here we begin by giving a new method for computing the supercorrelation functions of the chiral part of the stress-tensor supermultiplet by making use of twistor theory. We derive Feynman rules and graphical rules which involve a new set of building blocks which we can identify as a new class of N=4 off-shell superconformal invariants. This class of off-shell superconformal invariant is related to the known N=4 on-shell superconformal invariant pertinent to planar scattering amplitudes. We then move onto the six-point tree-level NMHV scattering amplitude. Previous results are given in terms of a manifestly dual superconformal invariant basis called the R-invariant. We define and analyse a generalisation of this invariant which contains half of the dual superconformal invariance. We apply it to the six-point tree-level NMHV scattering amplitude and find a new representation which manifestly contains half of the dual superconformal invariance and physical pole structure. This is in contrast to the R-invariant basis which manifests symmetry properties but does not manifest physical pole structures. Finally, we find the superconformal partial wave for four-point correlation functions of scalar operators on a super Grassmannian space (the space of m|n-planes in 2m|2n-dimensions) for theories with space-time symmetry SU(m,m|2n). This contains N=0,2,4 four-dimensional superconformal field theories in analytic superspace as well as a certain class of representations for the compact SU(2n) coset spaces. As an application we then specialise to N=4 supersymmetric Yang-Mills theory and use these results to perform a detailed superconformal partial wave analysis of the four-point functions of arbitrary weight half-BPS operators. We discuss the non-trivial separation of protected and unprotected sectors for the <2222>, <2233> and <3333> cases in an SU(N) gauge theory at finite N (where < ijkl > = < tr(W^i)tr(W^j)tr(W^k)tr(W^l) >). The <2233> correlator predicts a non-trivial protected twist four sector for <3333> which we can completely determine using the knowledge that there is one such protected twist-4 operator for each spin.

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Dimastrogiovanni, Emanuela. "Cosmological correlation functions in scalar and vector inflationary models." Doctoral thesis, Università degli studi di Padova, 2010. http://hdl.handle.net/11577/3427056.

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This thesis is centered on three main subjects within the theory of inflation and cosmological perturbations: loop corrections to the power spectrum of curvature fluctuations generated during inflation; evolution of cosmological fluctuations in anisotropic pre-inflationary cosmologies; statistical anisotropy and non-Gaussianity predictions of models of inflation populated with vector fields. Currently, what makes even more interesting the study of 2-nd and higher order corrections to cosmological correlation functions as well as the computation of higher-than-two order correlators, is the almost unprecedented chance to confront theories with new and increasingly accurate experimental data that will shed more light in the physics of the early Universe. In the context of loop calculations, we have computed the corrections arising from scalar-tensor interactions in models of single-field inflation (both for the standard slow-roll model and for models described by Lagrangians with non-canonical kinetic terms). In the context of anisotropic cosmologies, also motivated by the observation of ``anomalies'' in the Cosmic Microwave Background (CMB) fluctuations, we have computed the bispectrum and the trispectrum of the curvature fluctuations in inflationary models with SU(2) vector fields, analyzing the statistical anisotropy features of the correlators in these models; finally, we have studied cosmological perturbations for a Universe with a Bianchi type-I background metric, with an energy density dominated by a pressureless fluid and in the presence of a cosmological constant.
Questa tesi e' incentrata su tre argomenti principali che si collocano nella teoria dell'inflazione e delle perturbazioni cosmologiche: correzioni ad un loop per il power spectrum delle fluttuazioni di curvatura scalare prodotte durante l'inflazione; evoluzione delle perturbazioni in cosmologie anisotrope pre-inflazionarie; predizioni di non-Gaussianita' e di anisotropia statistica per modelli d'inflazione in presenza di campi vettoriali. Al momento, lo studio di correzioni al secondo ordine e oltre per funzioni di correlazioni cosmologiche, cosi' come il calcolo di correlatori di ordine superiore al secondo, sono resi ancora piu' interessanti dalla possibilita' di un confronto della teoria con nuovi e mai cosi' accurati dati sperimentali, che si spera aiuteranno nella comprensione della fisica dell'Universo primordiale. Nel contesto di calcoli a un loop, abbiamo calcolato le correzioni dovute alle interazioni scalari-gravitoni in modelli di single-field inflation (sia nel caso standard di slow-roll inflation sia per modelli con Lagrangiane dai termini cinetici non canonici). Nel constesto delle cosmologie anisotrope, motivate anche dal rilevamento di ``anomalie'' nelle fluttuazioni del Fondo Cosmico a Microonde (CMB), abbiamo calcolato il bispettro e il trispettro delle fluttuazioni della curvatura scalare in modelli inflazionari con campi vettoriali di tipo SU(2), studiandone le caratteristiche di anisotropia statistica; infine, abbiamo studiato le perturbationi cosmologiche per un Universo con una metrica di background di tipo Bianchi-I, con una densita' di energia dominata da un fluido non-collisionale e in presenza di una costante cosmologica.

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Kianifar, Mohammed R., and I. Felician Campean. "Performance evaluation of metamodelling methods for engineering problems: towards a practitioner guide." Springer, 2019. http://hdl.handle.net/10454/17192.

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Yes
Metamodelling or surrogate modelling techniques are frequently used across the engineering disciplines in conjunction with expensive simulation models or physical experiments. With the proliferation of metamodeling techniques developed to provide enhanced performance for specific problems, and the wide availability of a diverse choice of tools in engineering software packages, the engineering task of selecting a robust metamodeling technique for practical problems is still a challenge. This research introduces a framework for describing the typology of engineering problems, in terms of dimensionality and complexity, and the modelling conditions, reflecting the noisiness of the signals and the affordability of sample sizes, and on this basis presents a systematic evaluation of the performance of frequently used metamodeling techniques. A set of metamodeling techniques, selected based on their reported use for engineering problems (i.e. Polynomial, Radial Basis Function, and Kriging), were systematically evaluated in terms of accuracy and robustness against a carefully assembled set of 18 test functions covering different types of problems, sampling conditions and noise conditions. A set of four real-world engineering case studies covering both computer simulation and physical experiments were also analysed as validation tests for the proposed guidelines. The main conclusions drawn from the study are that Kriging model with Matérn 5/2 correlation function performs consistently well across different problem types with smooth (i.e. not noisy) data, while Kriging model with Matérn 3/2 correlation function provides robust performance under noisy conditions, except for the very high noise conditions, where the Kriging model with nugget appears to provide better models. These results provide engineering practitioners with a guide for the choice of a metamodeling technique for problem types and modelling conditions represented in the study, whereas the evaluation framework and benchmarking problems set will be useful for researchers conducting similar studies.

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Aichele, Martin. "Simulation studies of correlation functions and relaxation in polymeric systems." [S.l. : s.n.], 2003. http://deposit.ddb.de/cgi-bin/dokserv?idn=968908411.

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Le, Tuan Minh. "Infinite Volume Limit for Correlation functions in the Dipole Gas." Thesis, State University of New York at Buffalo, 2013. http://pqdtopen.proquest.com/#viewpdf?dispub=3565781.

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We consider a classical lattice dipole gas with low activity in dimension d ≥ 3. We study long distance properties by a renormalization group analysis. We prove that various correlation functions have a infinite volume limit. We also get estimates on the decay of correlation functions.

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25

Arzamasovs, Maksims. "Static and dynamic correlation functions in one-dimensional bose liquids." Thesis, University of Birmingham, 2014. http://etheses.bham.ac.uk//id/eprint/5483/.

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This Thesis discusses approaches to calculating static and dynamic correlation functions in onedimensional gases of interacting bosons. The first part of the Thesis deals with the momentummomentum correlation function in the weakly interacting 1D Bose gas. In the regime of phase fluctuating quasicondensate this correlator is found to differ qualitatively from the form predicted by Bogoliubov theory of the true condensate in that correlations between any two values of momentum become finite. Linear hydrodynamics used to calculate the quasicondensate correlation function prove to be adequate. A classical field approximation is used to smoothly interpolate between the quasicondensate and strongly degenerate gas regimes. In the second part the focus is shifted to the dynamical structure factor and it is shown that hydrodynamics is generally inapplicable to calculating the dynamical correlators. The hydrodynamic treatment is enhanced using impurity theory and an exact model-dependent boundary is obtained for the region of applicability of hydrodynamics on the momentum-energy plane. Numerical estimates show that non-hydrodynamic behavior should be observable for the currently available values of experimental parameters.

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26

Pereira, Raul. "Correlation Functions in Integrable Theories : From weak to strong coupling." Doctoral thesis, Uppsala universitet, Teoretisk fysik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-320811.

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The discovery of integrability in planar N=4 super Yang-Mills and ABJM has enabled a precise study of AdS/CFT. In the past decade integrability has been successfully applied to the spectrum of anomalous dimensions, which can now be obtained at any value of the coupling. However, in order to solve conformal field theories one also needs to understand their structure constants. Recently, there has been great progress in this direction with the all-loop proposal of Basso, Komatsu and Vieira. But there is still much to understand, as it is not yet possible to use that formalism to find structure constants of short operators at strong coupling. It is important to study wrapping corrections and resum them as the TBA did for the spectrum. It is also crucial to obtain perturbative data that can be used to check if the all-loop proposal is correct or if there are new structures that need to be unveiled. In this thesis we compute several structure constants of short operators at strong coupling, including the structure constant of Konishi with half-BPS operators. Still at strong coupling, we find a relation between the building blocks of superstring amplitudes and the tensor structures allowed by conformal symmetry. We also consider the case of extremal correlation functions and the relation of their poles to mixing with double-trace operators. We also study three-point functions at weak coupling. We take the OPE limit in a four-point function of half-BPS operators in order to shed some light on the structure of five-loop wrapping corrections of the Hexagon form factors. Finally, we take the first steps in the generalization of the Hexagon programme to other theories. We find the non-extremal setup in ABJM and the residual symmetry that it preserves, which we use to fix the two-particle form factor and constrain the four-particle hexagon. Finally, we find that the Watson equations hint at a dressing phase that needs to be further investigated.

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Srinivasan, Nirmala. "Cross-Correlation Of Biomedical Images Using Two Dimensional Discrete Hermite Functions." University of Akron / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=akron1341866987.

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28

Cai, Jia. "Learning gradients and canonical correlation by kernel methods /." access full-text access abstract and table of contents, 2009. http://libweb.cityu.edu.hk/cgi-bin/ezdb/thesis.pl?phd-ma-b23749349f.pdf.

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Thesis (Ph.D.)--City University of Hong Kong, 2009.
"Submitted to Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy." Includes bibliographical references (leaves [52]-58)

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Marcotte, Étienne. "First principles theory for quantum transport : effects of strong correlation." Thesis, McGill University, 2008. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=116102.

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In this work, we investigate effects of strong correlation to quantum transport from atomic first principles. In order to accomplish this task, we use a well established state-of-the-art formalism of quantum transport where density functional theory (DFT) is carried out within the Keldysh non-equilibrium Green's functions (NEGF). To deal with certain strong correlation phenomenon, we integrated an local density approximation plus Hubbard U (LDA+U) exchange-correlation potential into the existing NEGF-DFT formalism. The LDA+U potential correctly accounts for the electronic structure of correlated material. We will present the theory and numerical implementation associated with the NEGF-DFT-(LDA+U) in detail. Extensive tests on the well known correlated material FeO crystal have been carried out and results compared with previous literature as well as to experimental data.
We then apply our NEGF-DFT-(LDA+U) technique to investigate transport physics of spin resolved tunnelling in Fe/MgO/Fe magnetic tunnel junctions (MTJ). We found that interfacial oxygen atoms are enough to localise the 3d electrons of infacial Fe atoms due to strong correlation. This surprising result substantially changes quantum transport properties of the MTJ, in particular it reduces magnetic resistance ratio by about 33%. This strongly correlated physics is absent if the conventional local spin density approximation (LSDA) is used in the NEGF-DFT analysis. Results of LSDA and LDA+ U exchange-correlation potential will be compared. Furthermore, through investigating contributions to scattering states by various atomic orbitals, we clearly identify the reason why LDA+U changes quantum transport in both quantitative and qualitative ways. Finally, we believe this strongly correlated physics should be general in other MTJs involving different oxides.

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Matshawule, Siyambonga Donald. "Probing the large-scale structure of the universe with correlation functions." Thesis, University of the Western Cape, 2014. http://hdl.handle.net/11394/4280.

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>Magister Scientiae - MSc
In this project we explore a new statistical package called KSTAT that computes the 2PCF and higher order correlation functions, such as the 3PCF, on BOSS, making use of high performance computing facilities to improve optimization. The higher order statistics such as the 3PCF can be used to probe primordial non-Gaussianity. We present the first and most precise measurements of the reduced 3PCF (Q) measured using KSTAT on the DR10 data release at higher redshift, DR10 CMASS p z 0:5q and LOWZ p z 0:3q. Our reduced 3PCF results at low redshift z 0:3 are consistent with those of McBride et al. (2011a) at z 0:104 in the SDSS LRG sample. In this initial analysis, we have found no evidence of evolution of the 3PCF on small and large scales, however we do observe the characteristic U shape of the reduced 3PCF as one increases scale

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Gerstenlauer, Mischa [Verfasser], and Arthur [Akademischer Betreuer] Hebecker. "An Analysis of Inflationary Correlation Functions / Mischa Gerstenlauer ; Betreuer: Arthur Hebecker." Heidelberg : Universitätsbibliothek Heidelberg, 2011. http://d-nb.info/1179783263/34.

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Mumba, Mambwe. "EFFECTS OF COUPLING BETWEEN CENTER OF MASS MOTION OF AN ATOM AND A CAVITY MODE: PHOTON STATISTICS AND WAVE-PARTICLE CORRELATIONS." Connect to this document online, 2005. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=miami1121433361.

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Thesis (M.S.)--Miami University, Dept. of Physics, 2005.
Title from first page of PDF document. Document formatted into pages; contains [1], v, 296 p. : ill. Includes bibliographical references (p. 393-396).

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Di, Sabatino Stefano. "Reduced density-matrix functional theory : correlation and spectroscopy." Thesis, Toulouse 3, 2015. http://www.theses.fr/2015TOU30137.

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Cette thèse traite de la description de la corrélation électronique et de la spectroscopie dans le cadre de la Théorie de la Fonctionnelle de la Matrice Densité Réduite (RDMFT). Dans la RDMFT, les propriétés de l'état fondamental d'un système physique sont des fonctionnelles de la matrice densité à un corps. Plusieurs approximations à la corrélation électronique ont été proposées dans la littérature. Beaucoup d'entre elles peuvent être reliés au travail de Müller, qui en a proposé une similaire à l'approximation Hartree-Fock mais qui peut produire des nombres d'occupation fractionnaires. Cela n'est pas toujours suffisant, notamment dans les matériaux fortement corrélés. Par ailleurs, l'expression des observables du système en terme de la matrice densité n'est pas toujours connue. Tel est le cas, par exemple, pour la fonction spectrale, qui est liée aux spectres de photoémission. Dans ce cas, il y a des annulations d'erreur entre l'approximation à la corrélation électronique et l'approximation à l'observable, ce qui affaiblit la théorie. Dans cette thèse, nous recherchons des approximations plus précises en exploitant le lien entre les matrices densité et les fonctions de Green. Dans la première partie de la thèse, nous nous concentrons sur la fonction spectrale. En utilisant le modèle de Hubbard, qui peut être résolu exactement, nous analysons les approximations existantes à cette observable et nous soulignons leurs points faibles. Ensuite, à partir de sa définition en terme de la fonction de Green à un corps nous dérivons une expression pour la fonction spectrale qui dépend des nombres d'occupation naturels et d'une énergie efficace qui prend en compte toutes les excitations du système. Cette énergie efficace dépend de la matrice densité à un corps ainsi que des ordres supérieurs. Des approximations simples à cette énergie efficace donnent des spectres précis dans des systèmes modèles dans des régimes à la fois de faible et de forte corrélation. Pour illustrer notre méthode sur les matériaux réels, nous calculons le spectre de photoemission du NiO massif: notre méthode donne une image qualitativement correcte dans la phase antiferromagnétique et dans la phase paramagnétique, contrairement aux méthodes de champ moyen utilisés actuellement, qui donnent un métal dans le dernier cas. La deuxième partie de la thèse est plus explorative et traite des phénomènes dépendant du temps dans la RDMFT. En général, l'évolution temporelle des matrices densité est donnée par la hiérarchie des équations de Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY), dans lequel l'équation du mouvement de la matrice densité a n corps est donnée en termes de la matrice densité à n+1 corps. La première équation de la hiérarchie relie la matrice densité à un corps à la matrice densité à deux corps. La tâche difficile est de trouver des approximations à la matrice densité à deux corps. Les approximations existantes sont des extensions adiabatiques des approximations de l'état fondamental. Nous explorons cette question en examinant de nouvelles approximations qui nous tirons de la théorie à plusieurs corps (MBPT) basée sur les fonctions de Green ainsi que de la solution exacte du modèle de Anderson à deux niveaux dans son état fondamental. Nos premiers résultats sur le modèle de Anderson soumis à divers champs externes montrent quelques caractéristiques intéressantes, qui suggèrent d'explorer davantage ces approximations aussi sur des systèmes modèles plus grands
This thesis addresses the description of electron correlation and spectroscopy within the context of Reduced Density-Matrix Functional Theory (RDMFT). Within RDMFT the ground-state properties of a physical system are functionals of the ground-state reduced density matrix. Various approximations to electron correlation have been proposed in literature. Many of them, however, can be traced back to the work of Müller, who has proposed an approximation to the correlation which is similar to the Hartree-Fock approximation but which can produce fractional occupation numbers. This is not always sufficient. Moreover, the expression of the observables of the system in terms of the reduced density matrix is not always known. This is the case, for example, for the spectral function, which is closely related to photoemission spectra. In this case there are error cancellations between the approximation to correlation and the approximation to the observable, which weakens the theory. In this thesis we look for more accurate approximations by exploiting the link between density matrices and Green's functions. In the first part of the thesis we focus on the spectral function. Using the exactly solvable Hubbard model as illustration, we analyze the existent approximations to this observable and we point out their weak points. Then, starting from its definition in terms of the one-body Green's function, we derive an expression for the spectral function that depends on the natural occupation numbers and on an effective energy which accounts for all the charged excitations. This effective energy depends on the one-body as well as higher-order reduced density matrices. Simple approximations to this effective energy give accurate spectra in model systems in the weak as well as strong-correlation regimes. To illustrate our method on real materials we calculate the photoemission spectrum of bulk NiO: our method yields a qualitatively correct picture both in the antiferromagnetic and in the paramagnetic phases, contrary to currently used mean-field methods, which give a metal in the latter case. The second part of the thesis is more explorative and deals with time-dependent phenomena within RDMFT. In general the time evolution of the reduced density matrices is given by the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy of equations, in which the equation of motion of the n-body reduced density matrix is given in terms of the (n + 1)-body reduced density matrix. The first equation of the hierarchy relates the one-body to the two-body reduced density matrix. The difficult task is to find approximations to the two-body reduced density matrix. Commonly used approximations are adiabatic extension of ground-state approximations. We explore this issue by looking at new approximations derived from Many-Body Perturbation Theory (MBPT) based on Green's functions as well as from the exact solution of the two-level Anderson impurity model in its ground state. Our first results on the two-level Anderson model subjected to various external fields show some interesting and, at the same time, puzzling features, which suggest to explore further these approximations

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Cyrol, Anton Konrad [Verfasser], and Jan Martin [Akademischer Betreuer] Pawlowski. "Non-perturbative QCD Correlation Functions / Anton Konrad Cyrol ; Betreuer: Jan Martin Pawlowski." Heidelberg : Universitätsbibliothek Heidelberg, 2017. http://d-nb.info/1177689073/34.

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Stickan, Sven [Verfasser]. "Thermal Meson Properties from Correlation Functions and their Spectral Representation / Sven Stickan." Bielefeld : Universitätsbibliothek Bielefeld, 2003. http://d-nb.info/1034401130/34.

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Eden, Burkhard. "Correlation functions in N=2 and N=4 supersymmetric Yang-Mills theory." Thesis, King's College London (University of London), 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.312972.

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Nghiem, Son V. (Son Van). "Studies of correlation functions in random medium theory by Son V. Nghiem." Thesis, Massachusetts Institute of Technology, 1988. http://hdl.handle.net/1721.1/104471.

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38

Cyrol, Anton Konrad [Verfasser], and Jan M. [Akademischer Betreuer] Pawlowski. "Non-perturbative QCD Correlation Functions / Anton Konrad Cyrol ; Betreuer: Jan Martin Pawlowski." Heidelberg : Universitätsbibliothek Heidelberg, 2017. http://nbn-resolving.de/urn:nbn:de:bsz:16-heidok-237665.

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Troja, A. "ANGULAR HIGH-ORDER CORRELATION FUNCTIONS IN COSMOLOGY: LSS BISPECTRUM AND CMB TRISPECTRUM." Doctoral thesis, Università degli Studi di Milano, 2017. http://hdl.handle.net/2434/522720.

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High-order angular correlation functions and their harmonic counterpart, the polyspectra, offer a great opportunity to study the physics of spherical random fields. The best example of such a field is represented by the Cosmic Microwave Background (CMB) radiation, a relic from the hot phases of our Universe. But even the Large Scale Structure (LSS) as traced by galaxies can be treated in the same way when considering shells of iso-redshift. Both CMB and LSS are the most relevant source of cosmological information available today. This thesis offers a review of the analytical framework of spherical random distributions and polyspectra together with the now so-called standard cosmological model. The physics of inflation and the evolution of tiny quantum almost Gaussian fluctuations that eventually evolved into both CMB and LSS is also presented in details. The high-order angular polyspectra considered here are the Bispectrum and the Trispectrum. The former has been applied to LSS simulated data, the latter on CMB simulated data. The results of the analysis show that both of them could be useful in the next future in order to constrain cosmological parameters from real data. A three-year journey to understand how primordial fluctuations grew in the structures we see today.

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Mukherjee, Avijit. "Aspects of topological conformal field theory." Thesis, University of Cambridge, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.360757.

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Lolli, Linda. "Prolegomena for a comparative study of correlation functions in 2D integrable field theories." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/18144/.

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Questo lavoro di tesi si concentra sulla teoria dei Form Factors di operatori locali in due dimensioni. Si espone innanzitutto la teoria dello scattering fattorizzato, propria dei sistemi integrabili, per poi trattare sia classicamente che quantisticamente due modelli integrabili massivi, Sine-Gordon e Sinh-Gordon. Viene esposta l'algebra di Faddeev-Zamolodchikov, per mezzo di cui è possibile trovare lo spazio di Hilbert per modelli integrabili come spazio delle sue rappresentazioni. L'attenzione è infine posta sul regime in cui l'ampiezza relativa alla riflessione solitone-antisolitone nella matrice di scattering è nulla; tale caso si ottiene per valori particolari della costante di accoppiamento del modello di Sine-Gordon, coincidenti con i valori di soglia degli stati legati. Due proposte per l'espressione dei form factors per solitoni sono state prese in considerazione, avanzate una da Lukyanov, l'altra da Babelon, Bernard e Smirnov, tentando un confronto.

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Gülpers, Vera Magdalena [Verfasser]. "Hadronic correlation functions with quark-disconnected contributions in lattice QCD / Vera Magdalena Gülpers." Mainz : Universitätsbibliothek Mainz, 2015. http://d-nb.info/107680375X/34.

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Tran, Vuong-Viet. "Perturbative correlation functions and scattering amplitudes in planar N=4 supersymmetric Yang-Mills." Thesis, Durham University, 2018. http://etheses.dur.ac.uk/12642/.

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In this thesis, we study the integrands of a special four-point correlation function formed of protected half-BPS operators and scattering amplitudes in planar supersymmetric N=4 Yang-Mills. We use the "soft-collinear bootstrap" method to construct integrands of the aforementioned correlator and four-point scattering amplitudes to eight loops. Both have a unique representation in terms of (dual) conformal integrands with specified coefficients. The result is then extended to ten loops, by introducing two graphical relations, called the "triangle" and "pentagon" rules. These relations provide consistency conditions on the coefficients, and when combined with the "square" rule, prove sufficient to fix the answer to ten loops. We provide derivations for the graphical relations and illustrate their application with examples. The result exposes novel features seen for the first time at eight loops, that continue to be present through to ten loops. For example, the integrand includes terms that are finite even on-shell and terms that are divergent even off-shell (so-called "pseudoconformal" integrals). We then proceed to study the correlator/amplitude duality by taking six and seven adjacent points of the four-point correlator to be light-like separated. A conformal basis (with rational coefficients) is used to extract amplitude integrands for both six and seven particles up to two loops - more precisely, the complete one-loop amplitude and parity-even two-loop amplitude (at two loops, we use a refined prescriptive basis). We also construct an alternative six-point one-loop basis involving integrands with conformal cross-ratio coefficients, and reverse the duality to algebraically extract integrands from an ansatz, by introducing the Gram determinant. We expect the former approach to be applicable to n-points at arbitrary loop-order l, by going to one extra order of perturbation in the correlator (to determine all parity-odd l-loop ambiguities).

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Etherington, Carole J. "An analysis of cryptographically significant Boolean functions with high correlation immunity by reconfigurable computer." Thesis, Monterey, California. Naval Postgraduate School, 2010. http://hdl.handle.net/10945/5003.

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Approved for public release; distribution is unlimited
Boolean functions with high correlation immunity can be used in cryptosystems to defend against correlation attacks. These functions are rare and difficult to find. As the variables increase, this task becomes exponentially more complex and time consuming. Three different ways to execute a program to find the correlation immunity of a function are compared in this thesis. First, a program was written in C and executed on a conventional CPU. The same program was then executed on an FPGA on the SRC-6 reconfigurable computer. A similar program was written in Verilog and executed on the FPGA. By taking advantage of the parallel processing ability of the SRC-6, a wellprogrammed Verilog macro can find functions with high correlation immunity at a much faster rate. The SRC-6 reconfigurable computer is used in this thesis to find the correlation immunity of millions of functions up to six variables. Rotation symmetric and balanced functions were examined to find subsets that contain a high percentage of functions with good correlation immunity. The nonlinearity and correlation immunity of functions of four and five variables were compared to find functions with the best balance to fend off both correlation and linear attacks on a cryptosystem.

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FERRARI, LARISSA RANGEL. "SYNTACTIC PROCESSING IN THE ELDERLY: COMPREHENSION OF AMBIGUOUS SENTENCES AND CORRELATION WITH EXECUTIVE FUNCTIONS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2017. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=30748@1.

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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO
CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
Esta dissertação se insere na área da Psicolinguística, em articulação com a Neuropsicologia. A pesquisa se voltou para a investigação, em idosos hígidos, do processamento sintático de sentenças envolvendo ambiguidade temporária (ex.: Enquanto o homem cozinhava a batata era comprada no mercado), as quais induzem ao efeito labirinto (garden-path effect). O objetivo deste trabalho foi compreender em que medida um declínio de funções executivas com o avanço da idade poderia afetar o processamento desse tipo de estrutura sintática, a qual apresenta alta demanda para a memória de trabalho e parece requerer inibição de uma representação mental inicialmente possível. A pesquisa consistiu na aplicação de um experimento psicolinguístico de compreensão por leitura e testes de avaliação neuropsicológica (Span de Digítos, Stroop e Miniexame do Estado Mental, este último aplicado apenas aos idosos). No experimento psicolinguístico, foram tomadas como variáveis intrassujeitos plausibilidade e extensão da região ambígua entre o sintagma nominal crítico (a batata) e o ponto de desambiguização da sentença (era comprada). Foram testados 40 participantes (20 idosos e 20 jovens). Houve um efeito principal de plausibilidade e extensão da região ambígua e um efeito de interação entre grupo e plausibilidade, tendo os idosos apresentado maior dificuldade, nas condições plausíveis, para inibir a estrutura sintática equivocada construída inicialmente. Também observamos uma correlação entre plausibilidade e o teste Stroop. Os resultados são discutidos em termos da abordagem Good-Enough da compreensão da linguagem e de questões pertinentes às relações entre linguagem e outros domínios da cognição, em especial o papel de funções executivas no processamento sintático.
This master s thesis is situated within the area of psycholinguistics, in conjunction with neuropsychology, and investigates syntactic processing of temporarily ambiguous sentences in the elderly (While the man cooked the potatoes were bought at the supermarket.). These structures induce the garden-path effect. The purpose of the work was to analyze to what extent a decline in executive functions with advancing age could affect syntactic processing of syntactic ambiguity, which presents a high demand for working memory and seems to require inhibition of an initially possible mental representation. The research consisted in the application of a psycholinguistic experiment (a reading comprehension task) and neuropsychological evaluation tests (Digit Span, Stroop and Mini-Mental State Examination; the latter was only applied to the group of older participants). In the psycholinguistic experiment, plausibility and the distance between the critical noun phrase (the potato) and the point of disambiguation of the sentence (was bought) were taken as within-subjects variables. Forty participants (20 older adults and 20 young adults) were tested. A main effect of plausibility and distance and an interaction effect between group and plausibility were observed. The elderly showed more difficulty in inhibiting the initial misinterpretation when the sentence was plausible. There was also a correlation between plausibility and the Stroop test. The results are discussed in terms of the Good-Enough Approach to language comprehension and the relationship between language and other domains of cognition, especially the role of executive functions in syntactic processing.

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46

Hutsalyuk, Arthur [Verfasser]. "Non-perturbative approach to calculation of correlation functions in 1D Fermi gases / Arthur Hutsalyuk." Wuppertal : Universitätsbibliothek Wuppertal, 2019. http://d-nb.info/1204222207/34.

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Pavosevic, Fabijan. "Explicitly Correlated Methods for Large Molecular Systems." Diss., Virginia Tech, 2018. http://hdl.handle.net/10919/82000.

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Wave function based electronic structure methods have became a robust and reliable tool for the prediction and interpretation of the results of chemical experiments. However, they suffer from very steep scaling behavior with respect to an increase in the size of the system as well as very slow convergence of the correlation energy with respect to the basis set size. Thus these methods are limited to small systems of up to a dozen atoms. The first of these issues can be efficiently resolved by exploiting the local nature of electron correlation effects while the second problem is alleviated by the use of explicitly correlated R12/F12 methods. Since R12/F12 methods are central to this work, we start by reviewing their modern formulation. Next, we present the explicitly correlated second-order Mo ller-Plesset (MP2-F12) method in which all nontrivial post-mean-field steps are formulated with linear computational complexity in system size [Pavov{s}evi'c et al., {em J. Chem. Phys.} {bf 144}, 144109 (2016)]. The two key ideas are the use of pair-natural orbitals for compact representation of wave function amplitudes and the use of domain approximation to impose the block sparsity. This development utilizes the concepts for sparse representation of tensors described in the context of the DLPNO-MP2 method by Neese, Valeev and co-workers [Pinski et al., {em J. Chem. Phys.} {bf 143}, 034108 (2015)]. Novel developments reported here include the use of domains not only for the projected atomic orbitals, but also for the complementary auxiliary basis set (CABS) used to approximate the three- and four-electron integrals of the F12 theory, and a simplification of the standard B intermediate of the F12 theory that avoids computation of four-index two-electron integrals that involve two CABS indices. For quasi-1-dimensional systems (n-alkanes) the bigO{N} DLPNO-MP2-F12 method becomes less expensive than the conventional bigO{N^{5}} MP2-F12 for $n$ between 10 and 15, for double- and triple-zeta basis sets; for the largest alkane, C$_{200}$H$_{402}$, in def2-TZVP basis the observed computational complexity is $N^{sim1.6}$, largely due to the cubic cost of computing the mean-field operators. The method reproduces the canonical MP2-F12 energy with high precision: 99.9% of the canonical correlation energy is recovered with the default truncation parameters. Although its cost is significantly higher than that of DLPNO-MP2 method, the cost increase is compensated by the great reduction of the basis set error due to explicit correlation. We extend this formalism to develop a linear-scaling coupled-cluster singles and doubles with perturbative inclusion of triples and explicitly correlated geminals [Pavov{s}evi'c et al., {em J. Chem. Phys.} {bf 146}, 174108 (2017)]. Even for conservative truncation levels, the method rapidly reaches near-linear complexity in realistic basis sets; e.g., an effective scaling exponent of 1.49 was obtained for n-alkanes with up to 200 carbon atoms in a def2-TZVP basis set. The robustness of the method is benchmarked against the massively parallel implementation of the conventional explicitly correlated coupled-cluster for a 20-water cluster; the total dissociation energy of the cluster ($sim$186 kcal/mol) is affected by the reduced-scaling approximations by only $sim$0.4 kcal/mol. The reduced-scaling explicitly correlated CCSD(T) method is used to examine the binding energies of several systems in the L7 benchmark data set of noncovalent interactions. Additionally, we discuss a massively parallel implementation of the Laplace transform perturbative triple correction (T) to the DF-CCSD energy within density fitting framework. This work is closely related to the work by Scuseria and co-workers [Constans et al., {em J. Chem. Phys.} {bf 113}, 10451 (2000)]. The accuracy of quadrature with respect to the number of quadrature points has been investigated on systems of the 18-water cluster, uracil dimer and pentacene dimer. In the case of the 18-water cluster, the $mu text{E}_{text{h}}$ accuracy is achieved with only 3 quadrature points. For the uracil dimer and pentacene dimer, 6 or more quadrature points are required to achieve $mu text{E}_{text{h}}$ accuracy; however, binding energy of $<$1 kcal/mol is obtained with 4 quadrature points. We observe an excellent strong scaling behavior on distributed-memory commodity cluster for the 18-water cluster. Furthermore, the Laplace transform formulation of (T) performs faster than the canonical (T) in the case of studied systems. The efficiency of the method has been furthermore tested on a DNA base-pair, a system with more than one thousand basis functions. Lastly, we discuss an explicitly correlated formalism for the second-order single-particle Green's function method (GF2-F12) that does not assume the popular diagonal approximation, and describes the energy dependence of the explicitly correlated terms [Pavov{s}evi'c et al., {em J. Chem. Phys.} {bf 147}, 121101 (2017)]. For small and medium organic molecules the basis set errors of ionization potentials of GF2-F12 are radically improved relative to GF2: the performance of GF2-F12/aug-cc-pVDZ is better than that of GF2/aug-cc-pVQZ, at a significantly lower cost.
Ph. D.

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48

Wissel, Sönke. "Mesonic correlation functions from light quarks and their spectral representation in hot quenched lattice QCD." [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=982318332.

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Verdebout, Simon. "On the use of non-orthogonal partition correlation functions in atomic physics: theory and applications." Doctoral thesis, Universite Libre de Bruxelles, 2012. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209620.

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Our thesis tackles the many-electronic problem considering a non-relativistic and a relativistic orbital approach. Using the suites of programs ATSP and GRASP, we are able to approximate many-electron wave functions beyond the independent particle model by considering a superposition of CSFs. The optimization process, based on the variational principle, provides the best possible mixing coefficients fixing the linear combination of CSFs and spin-orbital basis on which we impose the orthonormality condition between functions of the same l or kappa subspace. Using this conventional approach within the relativistic framework, we estimate different properties of the triply ionized antimony atom (Sb IV), namely transition energies, transition probabilities, isotope shifts and a hyperfine-induced transition.

In the aim of partially relaxing the orthogonality constraints between correlation orbitals, we use the variational principle for targeting specific correlation effects by tailoring the configuration space. Independent sets of correlation orbitals, embedded in PCF, are produced from MCHF calculations. These non-orthogonal functions span CSF spaces that are coupled to each other by solving the associated generalized eigenvalue problem. The Hamiltonian and overlap matrix elements are evaluated using the biorthonormal orbital transformations and the efficient counter-transformations of the configuration interaction eigenvectors. This original method is successfully applied for describing different light atomic systems such as Li I, Be I, B I, C II and Ne I. An unwanted effect, called the ``constraint effect', is described and studied for these particular atomic systems. Even if this constraint can be completely relaxed through the DPCFI method, the computational resources required by such an approach lead us to study some simple strategies relaxing partially this constraint. This study takes it place in the context of neutral beryllium for which we test two particular strategies: one based on a weight criterion and one based on the type of excitations. Before concluding, we expose some developments combining the SCF process and the biorthonormal condition to relax the orthogonality constraints that are presently applied to the optimization process of the spin-orbital basis.

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Dans notre thèse, nous abordons le problème polyélectronique dans un contexte non-relativiste et relativiste en adoptant une approche orbitalaire. En utilisant les suites de programmes reconnues ATSP et GRASP, nous sommes aptes à approcher des fonctions d'ondes polyélectroniques au-delà du modèle des particules indépendantes en utilisant une superposition de CSFs. Le processus d'optimisation, basé sur le principe des variations, fournit la meilleure estimation possible des coefficients de mélange, fixant la combinaison linéaire de CSFs et la meilleure base de spin-orbitales sur laquelle on impose la condition d'orthonormalité entre les fonctions appartenant au même sous-espace l ou kappa. En adoptant cette approche dans un cadre relativiste, nous évaluons des énergies de transition, des probabilités de transition, des déplacements isotopiques ainsi qu'une transition induite par mélange hyperfin pour l'atome d'antimoine trois fois ionisé (Sb IV).

Dans le but de relâcher partiellement les contraintes d'orthogonalité entre les orbitales de corrélation, nous utilisons le principe des variations afin de cibler des effets précis de la corrélation en taillant l'espace des configurations. Les ensembles indépendants d'orbitales de corrélation sont obtenus via la méthode MCHF. Les espaces de CSFs, exprimés sur ces fonctions mono-électronique non-orthogonales, sont couplés en résolvant le problème aux valeurs propres généralisé associé. Les matrices Hamiltonienne et de recouvrement sont déterminées au moyen de la technique des transformations biorthonormales et de la contre-transformation des vecteurs propres associés. Cette méthode originale est utilisée avec succès pour décrire des systèmes atomiques légers comme Li I, Be I, B I, C II et Ne I. Un effet indésirable, appelé ``effet de contrainte', est déecrit et étudié pour ces derniers systèmes atomiques. Même si ces contraintes peuvent-être en principe totalement levées au travers de la méthode DPCFI, les ressources nécessaires à l'application de cette dernière approche nous ont conduit à la recherche de stratégies simples et efficaces autorisant leur levée partielle. Pour ce faire, dans le cadre de nos calculs réalisés sur l'atome de béryllium, nous avons envisagé deux stratégies particulières: l'une basée sur les coefficients de mélange et l'autre basée sur le type d'excitation. Avant de conclure, nous proposons quelques développements combinant le processus auto-cohérent et la condition de biorthonormalité dans le but de relâcher les contraintes d'orthogonalité appliquées lors du processus d'optimisation de la base de spin-orbitales.
Doctorat en Sciences de l'ingénieur
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Beichert, Felicitas. "Phases at complex temperature : spiral correlation functions and regions of Fisher zeros for Ising models." Thesis, University of St Andrews, 2013. http://hdl.handle.net/10023/3589.

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Abstract:

In this thesis we analyse the Fisher zeros for various Ising models. We show that there is long-range spiral order on the contours of zeros for classical one-dimensional Ising chains and that there is an imaginary “latent heat” associated with crossing those contours. Then we can see how areas of Fisher zeros fill in as we turn the Ising chain into Ising ladders of different widths, which seems to contradict the standard analysis presented in the literature and can be attributed to a different approach to the thermodynamic limit. Finally, we report results on frustrated two-dimensional classical Ising lattices, in particular the triangular and the kagomé lattice, and the quantum Ising problem.

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Dissertations / Theses on the topic 'Correlation functions'

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