Academic literature on the topic 'RPA [Approximation phase aléatoire]'
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Journal articles on the topic "RPA [Approximation phase aléatoire]"
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FETTER, A. L., C. B. HANNA, and R. B. LAUGHLIN. "ANYONS AND SUPERCONDUCTIVITY: RANDOM PHASE APPROXIMATION." International Journal of Modern Physics B 05, no. 16n17 (October 1991): 2751–90. http://dx.doi.org/10.1142/s0217979291001097.
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The two-dimensional ideal gas of particles obeying ν fractional statistics is recast as an interacting Fermi gas with long-range gauge potentials. A self-consistent dielectric description of the random phase approximation (RPA) provides a concise expression for the linear response of the fractional statistics gas to an external electromagnetic field. The RPA, believed to be correct for the present case of long-range interactions, yields two central results that are classic features of superconductivity: (1) a sharp undamped collective mode with a linear dispersion relation at long wavelengths: (2) a gauge-invariant Meissner effect in the transverse response to an external magnetic field.
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KHVESHCHENKO, D. V., and IAN I. KOGAN. "ANYON SUPERCONDUCTIVITY BEYOND THE RANDOM PHASE APPROXIMATION." International Journal of Modern Physics B 05, no. 14 (August 20, 1991): 2355–83. http://dx.doi.org/10.1142/s0217979291000924.
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We carry out a revision of the mechanism of anyon superconductivity found in the Random Phase Approximation. It is shown that the Debye screening of a statistical Coulomb-like interaction produced by contributions beyond the RPA destroys the abovementioned mechanism. The linear mode appeared in the particle-hole channel within the RPA is identified with a finite damping zero-sound. As an alternative mechanism an attraction of anyons which could lead to a formation of boson composites is observed. A finite temperature phase transition, hydrodynamics and electrodynamics of anyon system are described from this alternative point of view.
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DUKELSKY, J., and P. SCHUCK. "VARIATIONAL RANDOM PHASE APPROXIMATION FOR THE ANHARMONIC OSCILLATOR." Modern Physics Letters A 06, no. 26 (August 30, 1991): 2429–35. http://dx.doi.org/10.1142/s0217732391002852.
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The recently derived Variational Random Phase Approximation is examined using the anharmonoic oscillator model. Special attention is paid to the ground state RPA wave function and the convergence of the proposed truncation scheme to obtain the diagonal density matrix.
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Terasaki, J., A. Smetana, F. Šimkovic, and M. I. Krivoruchenko. "Reproduction of exact solutions of Lipkin model by nonlinear higher random-phase approximation." International Journal of Modern Physics E 26, no. 10 (October 2017): 1750062. http://dx.doi.org/10.1142/s0218301317500628.
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It is shown that the random-phase approximation (RPA) method with its nonlinear higher generalization, which was previously considered as approximation except for a very limited case, reproduces the exact solutions of the Lipkin model. The nonlinear higher RPA is based on an equation nonlinear on eigenvectors and includes many particle-many hole components in the creation operator of the excited states. We demonstrate the exact character of solutions analytically for the particle number [Formula: see text] and, numerically, for [Formula: see text]. This finding indicates that the nonlinear higher RPA is equivalent to the exact Schrödinger equation, which opens up new possibilities for realistic calculations in many-body problems.
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Zhang, Min-Ye, Zhi-Hao Cui, and Hong Jiang. "Relative stability of FeS2polymorphs with the random phase approximation approach." Journal of Materials Chemistry A 6, no. 15 (2018): 6606–16. http://dx.doi.org/10.1039/c8ta00759d.
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JOHNSON, CALVIN W., and IONEL STETCU. "SHORTCUTS TO NUCLEAR STRUCTURE: LESSONS IN HARTREE–FOCK, RPA, AND THE NO-CORE SHELL MODEL." International Journal of Modern Physics E 14, no. 01 (February 2005): 57–65. http://dx.doi.org/10.1142/s0218301305002771.
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While the no-core shell model is a state-of-the-art microscopic approach to low-energy nuclear structure, its intense computational requirements lead us to consider time-honored approximations such as the Hartree–Fock (HF) approximation and the random phase approximation (RPA). We review RPA and point out some common misunderstandings, then apply HF + RPA to the no-core shell model. Here the main issue is appropriate treatment of contamination by spurious center-of-mass motion.
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Taqi, Ali H., R. A. Radhi, and Adil M. Hussein. "Low excitations of 16O using generalized density matrix random phase approximation GDRPA." International Journal of Modern Physics E 23, no. 08 (August 2014): 1450038. http://dx.doi.org/10.1142/s0218301314500384.
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The random phase approximation (RPA) equations based on the generalized density matrix (GDM), the so-called GDRPA are reformulated in a more compact matrix form, which renders the method especially suitable for realistic nuclear structure calculations. The GDRPA Hamiltonian is expressed in terms of the one-body particle–particle (pp) and hole–hole (hh) density matrices, and the nuclear force contributes not only in the particle–hole (ph) channel, as in normal ph-RPA, but also in the pp and hh channels. The Hamiltonian is diagonalized iteratively starting from initial guess values and the iterating process is carried out until self-consistency is achieved. The calculation in the model space 1p, 1d and 2s using Warburton and Brown interaction WBP is performed for 16 O . The GDRPA in the ph shell model calculations is tested, by comparing the energy eigenvalues and the electron scattering form factors with the results of the normal RPA and with the available experimental data.
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Fan, J. D., and Y. M. Malozovsky. "Electron correlation effects beyond the random phase approximation." International Journal of Modern Physics B 30, no. 13 (May 19, 2016): 1642006. http://dx.doi.org/10.1142/s0217979216420066.
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The methods that have been used to deal with a many-particle system can be basically sorted into three types: Hamiltonian, field theory and phenomenological method. The first two methods are more popular. Traditionally, the Hamiltonian method has been widely adopted in the conventional electronic theory for metals, alloys and semiconductors. Basically, the mean-field approximation (MFA) that has been working well for a weakly coupled system like a metal is employed to simplify a Hamiltonian corresponding to a particular electron system. However, for a strongly coupled many-particle system like a cuprate superconductor MFA should in principle not apply. Therefore, the field theory on the basis of Green’s function and the Feynman diagrams must be invoked. In this method, one is however more familiar with the random phase approximation (RPA) that gives rise to the same results as MFA because of being short of the information for higher-order terms of interaction. For a strongly coupled electron system, it is obvious that one has to deal with higher-order terms of a pair interaction to get a correct solution. Any ignorance of the higher-order terms implies that the more sophisticated information contained in those terms is discarded. However, to date one has not reached a consensus on how to deal with the higher-order terms beyond RPA. We preset here a method that is termed the diagrammatic iteration approach (DIA) and able to derive higher-order terms of the interaction from the information of lower-order ones on the basis of Feynman diagram, with which one is able to go beyond RPA step by step. It is in principle possible that all of higher-order terms can be obtained, and then sorted to groups of diagrams. It turns out that each of the groups can be replaced by an equivalent one, forming a diagrammatic Dyson-equation-like relation. The diagrammatic solution is eventually “translated” to a four-dimensional integral equation. The method can be applied to a layered 2D system that is a model system of cuprate superconductors and others such as atomic, nuclear, heavy-fermion systems, etc.
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MARIANO, A. "THE NUMBER SELF-CONSISTENT RENORMALIZED RANDOM PHASE APPROXIMATION." International Journal of Modern Physics B 20, no. 30n31 (December 20, 2006): 5334–37. http://dx.doi.org/10.1142/s0217979206036442.
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RPA and its quasiparticle generalization (QRPA) have been widely used to study electromagnetic transitions and beta decays in medium and heavy nuclei, being the pn-QRPA charge exchange mode extensively employed in the description of single and double beta decays in vibrational nuclei. However develops a collapse, i.e. it presents imaginary eigen-values for strengths beyond a critical value of the force. Extensions called renormalized QRPA (RQRPA) do not develop any collapse going beyond the simplest quasiboson approximation, however they present several drawbacks which will be analyzed.
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AVDEENKOV, A. V., D. S. KOSOV, and A. I. VDOVIN. "RENORMALIZED RPA AT FINITE TEMPERATURE." Modern Physics Letters A 11, no. 10 (March 28, 1996): 853–59. http://dx.doi.org/10.1142/s0217732396000850.
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A method taking account of a deviation of state occupation numbers from the thermal RPA prescriptions is elaborated to study collective excitations in hot nuclei. This thermal renormalized random phase approximation (TRRPA) is from Ken-Ji Hara and D.J. Rowe. In developing the TRRPA, a formalism of the thermofield dynamics (TFD) is used. Some numerical results are given for the SU(2) model.
Dissertations / Theses on the topic "RPA [Approximation phase aléatoire]"
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Perez, Florent. "Plasmons dans un potentiel unidimensionnel : étude par spectroscopie Raman de fils quantiques gravés." Paris 6, 1998. http://www.theses.fr/1998PA066724.
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Rabhi, Aziz. "Approximation des phases aléatoires self-consistante dans l'étude de la superfluidité des systèmes fermioniques." Phd thesis, Université Claude Bernard - Lyon I, 2002. http://tel.archives-ouvertes.fr/tel-00003303.
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L'approximation de la phase aléatoire auto-cohérente (SCRPA) est une méthode qui permet d'inclure dans la théorie de champ moyen des corrélations dans l'état fondamental et les états excités. Elle constitue alors une méthode de type champ moyen pour les fluctuations quantiques. Elle a l'avantage de ne pas violer le principe de Pauli, contrairement à la RPA standard. qui, elle, est basée sur l'approximation dite de quasi-bosons. De plus, la SCRPA peut être formulée à partir d'un principe variationnel.Nous présentons la méthode SCRPA pour la description de la superfluidité dans les systèmes de fermions en utilisant sa version Quasi-particule (SCQRPA). Une étude détaillée de la transition de phase normale/superfluide ainsi que une discussion du mode mou qui enclenche la brisure de symétrie nombre de particules sont présentées. Comme application, nous avons traité le modèle d'appariement à deux niveaux qui est un modèle exactement soluble. Des bons résultats sont obtenus en comparaison avec les résultats exacts. La nature du mode spurieux dans la SCQRPA est identifiée. Une forte réduction de la fluctuation du nombre total de particules dans la SCQRPA par rapport à la méthode BCS est établie. La transition de la phase superfluide à la phase normale est soigneusement étudiée. Une nouvelle méthode de calcul des nombres d'occupation est présentée.
Le succès de la méthode SCQRPA est aussi présent dans le cas d'un modèle mélangeant fermions en bosons tel que le modèle de Da-Providencia-Schütte. Il subsiste cependant un problème concernant le mode spurieux qui doit être encore approfondi.
Dans le cas du modèle de la séniorité, on montre que la méthode SCQRPA permet d'une manière naturelle de restaurer la symétrie (nombre de particules) brisée au niveau de l'approximation de champ moyen. Ceci est réalisé par l'introduction d'un second paramètre de Lagrange qui fixe la variance de l'opérateur de symétrie à zéro. Cette caractéristique importante de la méthode SCQRPA est signalée pour la première fois.
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Hansen, Hubert. "Méthodes non-perturbatives en théorie quantique des champs : au-delà du champ moyen, l'approximation de la phase aléatoire." Phd thesis, Université Claude Bernard - Lyon I, 2002. http://tel.archives-ouvertes.fr/tel-00003814.
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L'étude de problèmes de physique hadronique dans le cadre de la théorie des champs nécessite l'emploi de méthodes non-perturbatives, les approches perturbatives ne pouvant s'appliquer pour QCD à basse énergie. L'équivalence formelle existant entre la théorie des champs et le problème à N corps nous a conduit à adapter des techniques non-perturbatives usuelles de la théorie du problème à N corps, comme l'approximation de champ moyen (ou approximation gaussienne) et l'approximation de la phase aléatoire (RPA).En se plaçant au-delà du champ moyen où seules sont prises en compte les corrélations entre une particule et un potentiel "moyen" à un corps, la RPA va permettre de rajouter dans le calcul de l'état fondamental des corrélations entre particules.
Afin de mettre en place le formalisme, on applique la RPA, sons différentes formes (standard, renormalisée, en termes de fonctions de Green), à l'une des plus simples théories des champs en interaction, la théorie scalaire lambda x phi^4. On montre qu'il se produit une transition de phase due à une brisure dynamique de symétrie dont le paramètre critique se rapproche des résultats obtenus sur réseaux et par la technique des "clusters". Les résultats sont aussi présentés à température finie pour le champ moyen.
On étudie également un modèle effectif réaliste de la transition de phase chirale, le modèle sigma-linéaire et on montre que le théorème de Goldstone est restauré, contrairement à l'approximation gaussienne.
Enfin pour éclaircir quelques points de la RPA et, aller au-delà des corrélations obtenues dans la forme renormalisée, on considère l'oscillateur anharmonique en mécanique quantique, en introduisant les corrélations minimales au-delà du champ moyen et on montre que les corrélations RPA améliorent grandement le résultat obtenu en champ moyen.
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Mussard, Bastien. "Modélisation quantochimiques des forces de dispersion de London par la méthode des phases aléatoires (RPA) : développements méthodologiques." Thesis, Université de Lorraine, 2013. http://www.theses.fr/2013LORR0292/document.
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Dans cette thèse sont montrés des développements de l'approximation de la phase aléatoire (RPA) dans le contexte de théories à séparation de portée. On présente des travaux sur le formalisme de la RPA en général, et en particulier sur le formalisme "matrice diélectrique" qui est exploré de manière systématique. On montre un résumé d'un travail sur les équations RPA dans le contexte d'orbitales localisées, notamment des développements des orbitales virtuelles localisées que sont les "orbitales oscillantes projetées" (POO). Un programme a été écrit pour calculer des fonctions telles que le trou de d'échange, la fonction de réponse, etc... sur des grilles de l'espace réel (grilles parallélépipédiques ou de type "DFT"). On montre certaines de ces visualisations. Dans l'espace réel, on expose une adaptation de l'approximation du dénominateur effectif (EED), développée originellement dans l'espace réciproque en physique du solide. Également, les gradients analytiques des énergies de corrélation RPA dans le contexte de la séparation de portée sont dérivés. Le formalisme développé ici à l'aide d'un lagrangien permet une dérivation tout-en-un des termes courte- et longue-portée qui émergent dans les expressions du gradient, et qui montrent un parallèle intéressant. Des applications sont montrées, telles que des optimisations de géométries aux niveaux RSH-dRPA-I et RSH-SOSEX d'un ensemble de 16 petites molécules, ou encore le calcul et la visualisation des densités corrélées au niveau RSH-dRPA-IIn this thesis are shown developments in the random phase approximation (RPA) in the context of range-separated theories. We present advances in the formalism of the RPA in general, and particularly in the "dielectric matrix" formulation of RPA, which is explored in details. We show a summary of a work on the RPA equations with localized orbitals, especially developments of the virtual localized orbitals that are the "projected oscillatory orbitals" (POO). A program has been written to calculate functions such as the exchange hole, the response function, etc... on real space grid (parallelepipedic or of the "DFT" type) ; some of those visualizations are shown here. In the real space, we offer an adaptation of the effective energy denominator approximation (EED), originally developed in the reciprocal space in solid physics. The analytical gradients of the RPA correlation energies in the context of range separation has been derived. The formalism developed here with a Lagrangian allows an all-in-one derivation of the short- and long-range terms that emerge in the expressions of the gradient. These terms show interesting parallels. Geometry optimizations at the RSH-dRPA-I and RSH-SOSEX levels on a set of 16 molecules are shown, as well as calculations and visualizations of correlated densities at the RSH-dRPA-I level
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Claudot, Julien. "Développements et applications de méthodes pour la description de l’énergie de corrélation dans les molécules et les solides." Thesis, Université de Lorraine, 2018. http://www.theses.fr/2018LORR0073/document.
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Les fonctionnelles de la densité couramment utilisées ont rencontrées un succès spectaculaire dans la modélisation des systèmes physiques, chimiques, et biologiques. Toutefois, elles se sont avérées inadaptées pour décrire certaines situations, comme par exemple les forces de dispersion de London ou les phénomènes de corrélation forte. Dans le cadre de cette thèse, nous nous sommes intéressés à des développements récents de la formulation de l’énergie de corrélation exprimée à partir du théorème de fluctuation-dissipation et connexion adiabatique, visant à pallier ces problèmes. En particulier, différentes implémentations des méthodes au-delà de l’approximation de la phase aléatoire, qui permettent la prise en compte de la contribution d’échange dans le calcul de l’énergie de corrélation, ont été comparées. Ensuite, afin de réduire drastiquement la complexité numérique, une procédure d’orthogonalisation des vecteurs utilisées pour représenter la matrice diélectrique a été développée. Ces méthodes ont ensuite été appliquées au calcul de l’énergie de liaison de petits complexes moléculaires. La formulation de l’énergie de corrélation de la théorie de perturbation de Møller-Plesset dans le contexte matrice diélectrique est aussi présentée et testée. En parallèle, des calculs utilisant les méthodes semi-empiriques numériquement efficaces ont été conduits sur trois ensembles de molécules afin d’en tester les performances concernant les énergies de liaisons en les comparant aux valeurs de références disponibles dans la littératureCommonly used density functionals have encountered a spectacular success in the modelling of physical, chemical or biological systems. However, they have proven to be unsuitable to describe some situations, such as London’s dispersion forces or strong correlation behaviour. In this thesis, we have been interested in recent developments in the formulation of the correlation energy from the adiabatic connection fluctuation dissipation theorem, to overcome these problems. In particular, different implementations of methods beyond the random phase approximation, which allow to take into account the exchange contribution in the computation of the correlation energy, have been compared. Then, in order to drastically decrease the numerical complexity, an orthogonalization procedure of the vectors used to represent the dielectric matrix has been developed. Then these approaches were applied to the calculation of the binding energy of small molecular complexes. The formulation of the correlation energy of the Møller-Plesset perturbation theory within the dielectric matrix context is also presented and tested. In parallel, calculations using numerically efficient semi-empirical methods were conducted over three molecular sets in order to test their performances regarding the binding energies by comparing them to reference values available in the literature
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Sengupta, Niladri. "Going beyond the Random Phase Approximation: A systematic assessment of structural phase transitions and interlayer binding energies." Diss., Temple University Libraries, 2018. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/513054.
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PhysicsPh.D.
The Random Phase Approximation and beyond Random Phase Approximation methods based on Adiabatic Connection Fluctuation Dissipation Theorem (ACFD) are tested for structural phase transitions of different groups of materials, including metal to metal, metal to semiconductor, semiconductor to semiconductor transitions. Also the performance assessment of semilocal density functionals with or without empirical long range dispersion corrections has been explored for the same cases. We have investigated the structural phase transitions of three broad group of materials, semi- conductor to metal transitions involving two symmetric structures, semiconductor to metal and wide bandgap semiconductor to semiconductor transitions involving at least one lower symmetric structure and lastly special cases comprising metal to metal transitions and transitions between energetically very close structural phases. The first group contains Si (diamond → β-tin), Ge (diamond → β-tin) and SiC (zinc blende → rocksalt), second group contains GaAs (zinc blende → cmcm) and SiO 2 (quartz → stishovite) and third group contains Pb (fcc → hcp), C(graphite → diamond) and BN (cubic → hexagonal) respectively. We have found that the difference in behavior of exchange and correlation in semilocal functionals and ACFD methods is striking. For the former, the exchange potential and energy often comprise the majority of the binding described by density functional approximations, and the addition of the correlation energy and potential often induce only a (relatively) small shift from the exchange- only results. For the ACFD, however, non self-consistent EXX typically underbinds by a considerable degree resulting in wildly inaccurate results. Thus the addition of correlation leads to very large shifts in the exchange-only results, in direct contrast to semilocal correlation. This difference in behavior is directly linked to the non-local nature of the EXX, and even though the exchange-only starting point is often nowhere close to experiment, the non-local correlation from the ACFD corrects this deficiency and yields the missing binding needed to produce accurate results. Thus we find the ACFD approach to be vital in the validation of semilocal results and recommend its use in materials where experimental results cannot be straightforwardly compared to other approximate electronic structure calculations. Utilizing the second-order approximation to Random Phase Approximation renormalized (RPAr) many-body perturbation theory for the interacting density-density response function, we have used a so-called higher-order terms (HOT) approximation for the correlation energy. In combination with the first-order RPAr correction, the HOT method faithfully captures the infinite- order correlation for a given exchange-correlation kernel, yielding errors of the total correlation energy on the order of 1% or less for most systems. For exchange-like kernels, our new method has the further benefit that the coupling-strength integration can be completely eliminated resulting in a modest reduction in computational cost compared to the traditional approach. When the correlation energy is accurately reproduced by the HOT approximation, structural properties and energy differences are also accurately reproduced, as confirmed by finding interlayer binding energies of several periodic solids and compared that to some molecular systems along with some phase transition parameters of SiC. Energy differences involving fragmentation have proved to be challenging for the HOT method, however, due to errors that do not cancel between a composite system and its constituent pieces which has been verified in our work as well.
Temple University--Theses
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Barillier-Pertuisel, Xavier. "Études de systèmes bosoniques et de mélanges boson-fermion à l'aide de l'Approximation des Phases Aléatoires." Paris 11, 2008. http://www.theses.fr/2008PA112371.
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La RPA, historiquement développée pour des fermions, est testée sur un système bosonique modèle, l'oscillateur anharmonique, pour vérifier sa pertinence sur des systèmes bosoniques non triviaux. Elle est ainsi appliquée au modèle de Richardson où des atomes bosoniques placés dans un piège peuvent former des états liés (molécules diatomiques). La RPA est ensuite appliquée à un mélange de boson fermion placé sur réseau optique unidimensionnel modélisé par un système de Bose-Fermi Hubbard. Selon l'intensité de l'interaction boson fermion, apparaît ou disparaît une discontinuité du nombre d'occupation (c'est-à-dire une surface de Fermi). Enfin, le formalisme de la matrice Test utilisé pour étudier le spectre d'excitation du système dans la limite thermodynamique. La densité d'état et la dépendance en impulsion du spectre convergent vers les résultats obtenus dans cette limite pour un nombre croissant de sites. L'intérêt de l'étude provient de l'apparition d'une branche particulière existant pour toute valeur attractive de l'interaction BF. Ce mode est interprété comme analogue au cas des paires BF du mode de Cooper et son existence est reliée à l'existence d'une surface de FermiOne of the recent and exciting aspects in the fields of cold atoms is the study of Bose-Fermi mixtures. Several boson-fermion mixtures have been realized and their properties have been theoretically studied using for instance Mean Field approximation or Quantum Monte Carlo (QMC) methods. The latter gives us exact results for one dimensional system. RPA, historically developed for fermions, is tested on a bosonic model, the anharmonic oscillator, to check its pertinence on non trivial bosonic systems. It's applied on the Richardson Model where trapped bosonic atoms can create bound states (diatomic molecules). Then RPA is applied to Bose Fermi mixtures located on a 1D optical lattice. In our work we consider BF pairing in a discrete environment of bosons and fully spin-polarized fermions. The system is modeled by a 1D Bose-Fermi Hubbard Hamiltonian with attractive BF interaction. One of the interests of such a system is to check th validity and limits of T-matrix approach, previously employed int he 3D case, by comparing with QMC results. We discuss the T-matrix approximation applied to a BF mixture for a discrete number of sites and show results obtained for the ground state energy, the excitation energies and occupation numbers. We discuss the continuous case underlining the appearance of a stable weak coupling BF pairing mode. This Cooper-pair-like mode exists at any small value of the interaction due to the presence of a Fermi surface
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Moghrabi, Kassem. "Beyond-mean-field corrections and effective interactions in the nuclear many-body problem." Phd thesis, Paris 11, 2013. http://tel.archives-ouvertes.fr/tel-00908607.
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Mean-field approaches successfully reproduce nuclear bulk properties like masses and radii within the Energy Density Functional (EDF) framework. However, complex correlations are missing in mean-field models and several observables related to single-particle and collective nuclear properties cannot be predicted accurately. The necessity to provide a precise description of the available data as well as reliable predictions in the exotic regions of the nuclear chart motivates the use of more sophisticated beyond-mean-field models. Correlations and higher-order corrections (beyond the leading mean-field order) are introduced. A crucial aspect in these calculations is the choice of the effective interaction to be used when one goes beyond the leading order (available effective interactions are commonly adjusted at the mean-field level). In the first part, we deal with the equation of state of nuclear matter evaluated up to the second order with the phenomenological Skyrme force. We analyze the ultraviolet divergence that is related to the zero range of the interaction and we introduce Skyrme-type regularized interactions that can be used at second order for matter. Cutoff regularization and dimen- sional regularization techniques are explored and applied. In the latter case, connections are naturally established between the EDF framework and some techniques employed in Effective Field Theories. In the second part, we check whether the regularized interactions introduced for nuclear matter can be employed also for finite nuclei. As an illustration, this analysis is performed within the particle- vibration model that represents an example of beyond mean-field models where an ultraviolet divergence appears if zero-range forces are used. These first applications suggest several directions to be explored to finally provide regularized interactions that are specially tailored for beyond- mean-field calculations for finite nuclei. Conclusions and perspectives are finally illustrated.
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Jemai, Mohsen. "Approximation des phases aleatoires self-consistante. Applications a des systemes de fermions fortement correles." Phd thesis, Université Paris Sud - Paris XI, 2004. http://tel.archives-ouvertes.fr/tel-00006530.
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Dans cette thèse nous avons appliqué la RPA auto-consistante (SCRPA) au modéle de Hubbard avec un petit nombre de sites (une chaîne à 2, 4, 6, ... sites). La SCRPA avait précédemment donné de très bon résultats dans d'autres modèles comme le modèle d'appariement de Richardson. Il était donc intéressant de voir quel genre de résultats la méthode allait produire pour un modèle plus complexe comme le modèle de Hubbard. A notre grande satisfaction le cas à 2 sites et deux électrons (demi-remplissage) est résolu exactement par la SCRPA. Ceci peut sembler un peu trivial mais le fait est que d'autres approximations toute à fait respectables telles que la "GW" ou l'approche avec la fonction d'onde de Gutzwiller restent loin du compte. Avec ce bon point de départ le cas à 6 sites a été regardé ensuite. Pour ce cas la SCRPA n'est, évidemment, plus exacte, cependant les résultats SCRPA s'en écartent uniquement de très peu sur une grande plage de valeurs de la constante de couplage U et notamment dans la région de la transition de phase vers un état avec magnétisation non nulle. Ceci est vrai pour l'énergie du fondamental, les excitations et les nombres d'occupations. On peut considérer cela comme un bon succès de la théorie. Cependant, le cas à 4 sites (plaquette), comme tous les cas à 4n sites, pose un problème à cause d'une dégénérescence au niveau Hartree-Fock. Une généralisation de la présente méthode en incluant en plus des paires, des quadruples opérateurs de Fermions (seconde RPA) est proposée pour traiter ces cas dans la présente approche. En effet pour une plaquette, on peut ainsi également retrouver le résultat exact. C'est donc une perspective intéressante de ce travail.
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Vast, Nathalie. "Etude ab initio des propriétés physiques des matériaux." Habilitation à diriger des recherches, Université Pierre et Marie Curie - Paris VI, 2009. http://tel.archives-ouvertes.fr/tel-00440923.
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Mon activité de recherche fondamentale dans le groupe de théorie du Laboratoire des Solides Irradiés concerne l'étude des propriétés des matériaux d'intérêt pour le CEA, dans les domaines du nucléaire ou de la nanoélectronique. Elle a pour objectif d'atteindre une description théorique -sans paramètre ajustable- des processus contrôlant l'excitation électronique, ainsi que la relaxation -ou désexcitation- électronique, et couvre: - Les propriétés de la matière hors excitation - l'état fondamental; - Les propriétés de l'état excité, abordées sous l'angle de la spectroscopie pour les électrons de valence; - Les vibrations collectives des atomes, leur couplage avec les électrons, et leurs effets sur le transport électronique ou la relaxation électronique. Ces études requièrent un environnement de calcul intensif et l'accès aux ordinateurs du Grand Equipement National de Calcul Intensif GENCI. Dans ce manuscrit, est d'abord rappelé comment calculer la fonction diélectrique inverse en théorie de la fonctionnelle de la densité dépendante du temps, et quel est le lien avec la fonction de perte électronique observée. Des résultats théoriques sur la fonction diélectrique inverse dans des oxydes non corrélés représentés par le dioxyde de titane TiO$_2$ et la zircone ZrO$_2$ sont décrits. Ensuite sont donnés les principaux résultats théoriques pour les calculs de spectres d'absorption optique pour l'oxyde de cuivre Cu$_2$O et la zircone ZrO$_2$. J'y présente une nouvelle interprétation de travail sur le noyau permettant de modéliser les effets excitoniques en théorie de la fonctionnelle de la densité dépendante du temps. Enfin, les derniers calculs menés sur les carbures de bore sont rappelés.
Books on the topic "RPA [Approximation phase aléatoire]"
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Horing, Norman J. Morgenstern. Random Phase Approximation Plasma Phenomenology, Semiclassical and Hydrodynamic Models; Electrodynamics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0010.
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Chapter 10 reviews both homogeneous and inhomogeneous quantum plasma dielectric response phenomenology starting with the RPA polarizability ring diagram in terms of thermal Green’s functions, also energy eigenfunctions. The homogeneous dynamic, non-local inverse dielectric screening functions (K) are exhibited for 3D, 2D, and 1D, encompassing the non-local plasmon spectra and static shielding (e.g. Friedel oscillations and Debye-Thomas-Fermi shielding). The role of a quantizing magnetic field in K is reviewed. Analytically simpler models are described: the semiclassical and classical limits and the hydrodynamic model, including surface plasmons. Exchange and correlation energies are discussed. The van der Waals interaction of two neutral polarizable systems (e.g. physisorption) is described by their individual two-particle Green’s functions: It devolves upon the role of the dynamic, non-local plasma image potential due to screening. The inverse dielectric screening function K also plays a central role in energy loss spectroscopy. Chapter 10 introduces electromagnetic dyadic Green’s functions and the inverse dielectric tensor; also the RPA dynamic, non-local conductivity tensor with application to a planar quantum well. Kramers–Krönig relations are discussed. Determination of electromagnetic response of a compound nanostructure system having several nanostructured parts is discussed, with applications to a quantum well in bulk plasma and also to a superlattice, resulting in coupled plasmon spectra and polaritons.
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Morawetz, Klaus. Approximations for the Selfenergy. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797241.003.0010.
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The systematic expansion of the selfenergy is presented with the help of the closure relation of chapter 7. Besides Hartree–Fock leading to meanfield kinetic equations, the random phase approximation (RPA) is shown to result into the Lennard–Balescu kinetic equation, and the ladder approximation into the Beth–Uehling–Uhlenbeck kinetic equation. The deficiencies of the ladder approximation are explored compared to the exact T-matrix by missing maximally crossed diagrams. The T-matrix provides the Bethe–Salpeter equation for the two-particle correlation functions. Vertex corrections to the RPA are presented. For a two-dimensional example, the selfenergy and effective mass are calculated. The structure factor and the pair-correlation function are introduced and calculated for various approximations.
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Horing, Norman J. Morgenstern. Non-Equilibrium Green’s Functions: Variational Relations and Approximations for Particle Interactions. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0009.
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Chapter 09 Nonequilibrium Green’s functions (NEGF), including coupled-correlated (C) single- and multi-particle Green’s functions, are defined as averages weighted with the time-development operator U(t0+τ,t0). Linear conductivity is exhibited as a two-particle equilibrium Green’s function (Kubo-type formulation). Admitting particle sources (S:η,η+) and non-conservation of number, the non-equilibrium multi-particle Green’s functions are constructed with numbers of creation and annihilation operators that may differ, and they may be derived as variational derivatives with respect to sources η,η+ of a generating functional eW=TrU(t0+τ,t0)CS/TrU(t0+τ,t0)C. (In the non-interacting case this yields the n-particle Green’s function as a permanent/determinant of single-particle Green’s functions.) These variational relations yield a symmetric set of multi-particle Green’s function equations. Cumulants and the Linked Cluster Theorem are discussed and the Random Phase Approximation (RPA) is derived variationally. Schwinger’s variational differential formulation of perturbation theories for the Green’s function, self-energy, vertex operator, and also shielded potential perturbation theory, are reviewed. The Langreth Algebra arises from analytic continuation of integration of products of Green’s functions in imaginary time to the real-time axis with time-ordering along the integration contour in the complex time plane. An account of the Generalized Kadanoff-Baym Ansatz is presented.
Book chapters on the topic "RPA [Approximation phase aléatoire]"
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Fai, Lukong Cornelius. "Random Phase Approximation (RPA)." In Quantum Field Theory, 133–74. Boca Raton, FL : CRC Press, Taylor & Francis Group, [2019]: CRC Press, 2019. http://dx.doi.org/10.1201/9780429196942-7.
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Schirmer, Jochen. "Random-Phase Approximation (RPA)." In Lecture Notes in Chemistry, 223–37. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-93602-4_15.
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"Random Phase Approximation (RPA)." In Greensche Funktionen in Festkörper- und Vielteilchenphysik, 162–227. Weinheim, FRG: Wiley-VCH Verlag GmbH & Co. KGaA, 2005. http://dx.doi.org/10.1002/3527603387.ch7.
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Boothroyd, Andrew T. "Magnetic Excitations." In Principles of Neutron Scattering from Condensed Matter, 257–310. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198862314.003.0008.
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In this chapter, the neutron inelastic scattering spectrum is calculated for a variety of magnetic systems. A number of isolated magnetic systems are considered, including single-ion crystal field and intermultiplet excitations, and magnetic clusters. Linear spin-wave theory, a method for calculating the collective spin dynamics in magnetically ordered systems, is outlined and applied to ferromagnets and antiferromagnets both with and without anisptropy. The Random Phase Approximation (RPA) method for the generalized susceptibility is presented and applied to calculate the spectrum of crystal field excitons in praseodymium. The nature of the spin excitations in itinerant magnets is described, and the generalized susceptibility is calculated in the RPA for itinerant electrons with echange correlations. General features of the spin dynamical response in quantum magnets are described, and illustrated by the magnetic spectra of quantum spin chains.
Conference papers on the topic "RPA [Approximation phase aléatoire]"
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Fiddy, Michael A., Hossein Alisafaee, and Raphael Tsu. "Designing low index metamaterials and the random phase approximation (RPA)." In 2014 International Conference on Electromagnetics in Advanced Applications (ICEAA). IEEE, 2014. http://dx.doi.org/10.1109/iceaa.2014.6903859.
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