Dissertations / Theses: 'Many-particle system'

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Yin, Qitao [Verfasser], and Li [Akademischer Betreuer] Chen. "Mean field limit of many particle system with non-Lipschitz force / Qitao Yin ; Betreuer: Li Chen." Mannheim : Universitätsbibliothek Mannheim, 2019. http://d-nb.info/1192664019/34.

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Winkler, Anton. "Analytic approaches to stochastic many-particle systems." Diss., lmu, 2012. http://nbn-resolving.de/urn:nbn:de:bvb:19-151131.

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Dammer, Stephan M. "Stochastic many-particle systems with irreversible dynamics." [S.l. : s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=974953334.

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Dammer, Stephan Markus. "Stochastic many-particle systems with irreversible dynamics." Gerhard-Mercator-Universitaet Duisburg, 2005. http://www.ub.uni-duisburg.de/ETD-db/theses/available/duett-01282005-115619/.

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In this thesis, several stochastic models are investigated, which are subjected to irreversible dynamics. Motivation for the presented work stems, on the one hand, from particular physical systems under consideration, which are modeled by the studied stochastic processes. Besides that, the models discussed in this thesis are, on the other hand, generally interesting from the point of view of statistical physics, since they describe systems far from thermodynamic equilibrium. Interesting properties to be encountered are, e.g., dynamical scaling behavior or continuous phase transitions. The first issue to be addressed, is the investigation of irreversibly aggregating systems, where the main emphasis is laid on aggregation of monopolarly charged clusters suspended in a fluid. For this purpose, rate equations are analyzed and Brownian dynamics simulations are performed. It is shown that the system crosses over from power-law cluster growth to sub-logarithmic cluster growth. Asymptotically, the cluster size distribution evolves towards a universal scaling form, which implies a 'self-focussing' of the size distribution. Another emphasis of this thesis is the investigation of nonequilibrium critical phenomena, in particular, the study of phase transitions into absorbing states (states that may be reached irreversibly). To this end, the continuous nonequilibrium phase transition of directed percolation, which serves as a paradigm for absorbing-state phase transitions, is analyzed by a novel approach. Despite the lack of a partition function for directed percolation, this novel approach follows the ideas of Yang-Lee theory of equilibrium statistical mechanics, by investigating the complex roots of the survival probability. Stochastic models such as directed percolation mimic spreading processes, e.g., the spreading of an infectious disease. The effect of long-time memory, which is not included in directed percolation and which corresponds to immunization in epidemic spreading, is investigated through an appropriate model. This model includes dynamical percolation (perfect immunization) as a special case, as well as directed percolation (no immunization). The critical behavior of this model is studied by means of Monte Carlo simulations, in particular for weak immunization. A further generalization is investigated, which allows spontaneous mutations and different species of spreading agents (pathogens). Restricting the analysis to perfect immunization and two spatial dimensions, it is shown by Monte Carlo simulations, that immunization leads to a crossover from dynamical to directed percolation. Other properties of this model are discussed in detail.

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Blois, Cindy Marie. "Functional integral representations for quantum many-particle systems." Thesis, University of British Columbia, 2015. http://hdl.handle.net/2429/54193.

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Formal functional integrals are commonly used as theoretical tools and as sources of intuition for predicting phase transitions of many-body systems in Condensed Matter Physics. In this thesis, we derive rigorous versions of these functional integrals for two types of quantum many-particle systems. We begin with a brief review of quantum statistical mechanics in Chapter 2 and the formalism of coherent states in Chapter 3, which form the basis for our analysis in Chapters 4 and 5. In Chapter 4, we study a mixed gas of bosons and/or fermions interacting on a finite lattice, with a general Hamiltonian that preserves the total number of particles in each species. We rigorously derive a functional integral representation for the partition function, which employs a large-field cutoff for the boson fields. We then expand the resulting “action” in powers of the fields and find a recursion relation for the coefficients. In the case of a two-body interaction (such as the Coulomb interaction), we also find bounds on the coefficients, which give a domain of analyticity for the action. This domain is large enough for use of the action in the functional integral, provided that the large-field cutoffs are taken to grow not too quickly. In Chapter 5, we study a system of electrons and phonons interacting in a finite lattice, using the Holstein Hamiltonian. Again, we rigorously derive a coherent-state functional integral representation for the partition function of this system and then prove that the “action” in the functional integral is an entire-analytic function of the fields. However, since the Holstein Hamiltonian does not preserve the total number of bosons, the approach from Chapter 4 requires some modification. In particular, we repeatedly use Duhamel expansions in powers of the interaction, rather than sums over particle numbers.
Science, Faculty of
Mathematics, Department of
Graduate

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Kerner, Joachim Friedrich. "Interacting many-particle systems on general compact quantum graphs." Thesis, University of London, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.603454.

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In this thesis, we discuss many-particle systems on general compact quantum graphs. The results cover systems of distinguishable particles as well as systems of bosons or fermions. The main focus lies on the introduction of many-particle interactions in order to establish a useful model regarding many-particle quantum chaos 811d onc-dimensional Bose-Einstein condensation (BEC). Using suitable quadratic forms, we will characterise self-adjoint realisations of the two- and many-particle Laplacian which incorporate two different types of interactions, i.e. singular interactions localised at the vertices of the graph and contact interactions which are also present along the edges. In that context, we will establish regularity results in order to characteristic the domains of the self-adjoint realisations explicitly. We will also discuss spectral properties of the constructed operators by establishing discreteness of their spectra and Weyl laws for the corresponding eigenvalue counts. Finally, based on the introduced models of interacting particles, we discuss BoseEinstein condensation on general quantum graphs. We will distinguish between systems of bosons for which BEC occurs and such for which no BEC is present at any finite temperature. As a final result, we prove that no Bose-Einstein condensation occurs (in the sense of phase transitions) in a system of bosons interacting via repulsive hard-core interactions.

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Rulands, Steffen. "Heterogeneity and spatial correlations in stochastic many-particle systems." Diss., Ludwig-Maximilians-Universität München, 2013. http://nbn-resolving.de/urn:nbn:de:bvb:19-173338.

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Børkje, Kjetil. "Theoretical Studies of Unconventional Order in Quantum Many-Particle Systems." Doctoral thesis, Norwegian University of Science and Technology, Department of Physics, 2008. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-2013.

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Nikolaev, Valentin. "Many-particle correlations in quasi-two-dimensional electron-hole systems." Thesis, University of Exeter, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.248096.

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Zhang, Ge. "Exotic Ordered and Disordered Many-Particle Systems with Novel Properties." Thesis, Princeton University, 2017. http://pqdtopen.proquest.com/#viewpdf?dispub=10622528.

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This dissertation presents studies on several statistical-mechanical problems, many of which involve exotic many-particle systems. In Chapter 2, we present an algorithm to generate Random Sequential Addition (RSA) packings of hard hyperspheres at the infinite-time saturation limit, and investigate this limit with unprecedented precision. In Chapter 3, we study the problem of devising smooth, short-ranged isotropic pair potentials such that their ground state is an unusual targeted crystalline structure. We present a new algorithm to do so, and demonstrate its capability by targeting several singular structures that were not known to be achievable as ground states with isotropic interactions.

A substantial portion of this dissertation examines exotic many-particle systems with so-called “collective-coordinate” interactions. They include “stealthy” potentials, which are isotropic pair potentials with disordered and infinitely degenerate ground states as well as “perfect-glass” interactions, which have up to four-body contributions, and possess disordered and unique ground states, up to trivial symmetry operations. Chapters 4-7 study the classical ground states of “stealthy” potentials. We establish a numerical means to sample these infinitely-degenerate ground states in Chapter 4 and study exotic “stacked-slider” phases that arise at suitable low densities in Chapter 5. In Chapters 6 and 7, we investigate several geometrical and physical properties of stealthy systems. Chapter 8 studies lattice-gas systems with the same stealthy potentials. Chapter 9 is concerned with the introduction and study of the perfect-glass paradigm. Chapter 10 demonstrates that perfect-glass interactions indeed possess disordered and unique classical ground states—a highly counterintuitive proposition.

In Chapter 11, we use statistical-mechanical methods to characterize the spatial distribution of the prime numbers. We show that the primes are much more ordered than anyone previously thought via the structure factor. Indeed, they are characterized by infinitely many Bragg peaks in any non-zero interval of wave vectors, yet unlike quasicrystals, the ratio between the heights or locations of any two Bragg peaks is always rational. We analytically explain the locations and heights of all such peaks.

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Endres, Manuel. "Probing correlated quantum many-body systems at the single-particle level." Diss., lmu, 2013. http://nbn-resolving.de/urn:nbn:de:bvb:19-155062.

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Alarcón, Pardo Alfonso. "Quantum many-particle electron transport in time-dependent systems with Bohmian trajectories." Doctoral thesis, Universitat Autònoma de Barcelona, 2011. http://hdl.handle.net/10803/42002.

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Es conocido que a escalas nanométricas se debe tratar con en el problema de muchas partículas a la hora de estudiar dispositivos electrónicos. Es estos escenarios, la ecuación de Schrödinger dependiente del tiempo para muchas partículas solo se puede resolver para unos pocos grados de libertad. En este sentido, diferentes formalismos han sido desarrollados en la literatura (tales como time-dependent Density Functional Theory, Green's functions técnicas o Quantum Monte Carlo técnicas) para tratar sistemas cuánticos de muchos electrones. Estas aproximaciones modelizan de forma razonable el transporte electrónico en sistemas de muchas partículas. Una propuesta alternativa ha sido desarrollada por el Dr. Oriols para descomponer la ecuación de Schrödinger de N-partículas en un sistema de N-ecuaciones de Schrödinger para una sola partícula usando trayectorias (cuánticas) de Bohm. Basado en esta propuesta se presenta un 3D, general, versátil y dependiente del tiempo simulador de transporte de dispositivos electrónicos llamado BITLLES (Bohmian Interacting Transport for non-equiLibrium eLEctronic Structures). Las novedades que aporta el simulador BITLLES se basan en dos puntos. El primero, éste representa un modelo de transporte cuántico de electrones para muchas partículas en el cual se tiene en cuenta de forma explicita las correlaciones de Coulomb y de intercambio entre electrones usando trayectorias de Bohm. En segundo lugar, el simulador proporciona una completa información de los momentos de la corriente (i.e., DC, AC, fluctuaciones o incluso momentos mayores). A continuación resumimos las contribuciones que esta tesis aporta al desarrollo del simulador BITLLES. De esta forma, introducimos de forma explicita la interacción de intercambio entre electrones. En este contexto, mostramos como la interacción de intercambio es la responsable final para determinar la corriente total a través del sistema. Además presentamos una nueva aproximación para estudiar sistemas de muchas partículas donde los espines de los electrones tienen diferente orientación. Hasta donde llega nuestro conocimiento, es la primera vez que la interacción de intercambio es introducida de forma práctica en un simulador de transporte de electrones. Además presentamos la computación de la corriente total dependiente del tiempo en un contexto de alta frecuencia donde se tienen que tener en cuenta las variaciones del campo eléctrico dependientes del tiempo (i.e., la corriente de desplazamiento) para asegurar la conservación de la corriente. También discutimos el cálculo de la corriente total (conducción más desplazamiento) usando los teoremas de Ramo-Shockley-Pellegrini. Diferentes capacidades del simulador BITLLES como AC y fluctuaciones de la corriente se presentan para el diodo túnel resonante. También hemos usado el simulador BITLLES para testear un nuevo tipo de dispositivo nanoeléctronico diseñado para procesar señales dentro del espectro de los THz. Hemos llamado a este dispositivo Driven Tunneling Device. Se trata de un dispositivo de tres terminales donde la conductancia entre el drain y el source se controla por el terminal del gate el cual oscila a frecuencias de THz. También presentamos ejemplos prácticos de la funcionalidad de este dispositivo como un rectificador y un multiplicador de frecuencia. Finalmente, hemos desarrollado una aproximación numérica para resolver la ecuación de Schrödinger usando el modelo de tight-binding con el propósito de mejorar la descripción de la estructura de bandas del simulador BITLLES.
It is known that at nanoscale regime we must deal with the many-particle problem in order to study electronic devices. In this scenario, the time-dependent many-particle Schrödinger equation is only directly solvable for very few degrees of freedom. However, there are many electrons (degrees of freedom) in any electron device. In this sense, many-particle quantum electron formalisms (such as time-dependent Density Functional Theory, Green's functions techniques or Quantum Monte Carlo techniques) have been developed in the literature to provide reasonable approximations to model many-particle electron transport. An alternative proposal has been developed by Dr. Oriols to decompose the N-particle Schrödinger equation into a N-single particle Schrödinger equation using Bohmian trajectories. Based on this proposal a general, versatile and time-dependent 3D electron transport simulator for nanoelectronic devices, named BITLLES (Bohmian Interacting Transport for non-equiLibrium eLEctronic Structures) is presented. The novelty of the BITLLES simulator is based on two points. First, it presents a many-particle quantum electron transport model taking into account explicitly the Coulomb and exchange correlations among electrons using Bohmian trajectories. Second, it provides full information of the all current distribution moments (i.e. DC, AC, fluctuations and even higher moments). We summarize the important contributions of this thesis to the development of BITLLES simulator. Thus, we introduce explicitly the exchange correlations among electrons. In this context, we show how exchange interaction is the final responsible for determining the total current across the system. We also present a new approximation to study many-particle systems with spin of different orientations. Some practical examples are studied taking into account the exchange interaction. To the best of our knowledge, it is the first time that the exchange interaction is introduced explicitly (imposing the exchange symmetry properties directly into the many-particle wavefunction) in practical electron transport simulators. We present the computation of the time-dependent total current in the high-frequency regime where one has to compute time-dependent variations of the electric field (i.e. the displacement current) to assure current conservation. We discuss the computation of the total (conduction plus displacement) current using Bohmian trajectories and the Ramo-Shockley-Pellegrini theorems. Different capabilities of BITLLES simulator such as AC and current fluctuations are presented for Resonant Tunneling Devices. We have used the BITLLES simulator to test a new type of nanoelectronic device designed to process signals at THz regime named Driven Tunneling Device. It is a three terminal device where the drain-source conductance is controlled by a gate terminal that can oscillate at THz frequencies. We also present practical examples on the functionality of this device such as rectifier and frequency multiplier. Finally, we have developed a numerical approximation to solve the Schrödinger equation using tight-binding model to improve the band structure description of the BITLLES simulator.

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Cho, Kyeongjae 1963. "New methods for the calculation of dynamical properties of many-particle systems." Thesis, Massachusetts Institute of Technology, 1994. http://hdl.handle.net/1721.1/11917.

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Pfeifer, Jens Christian [Verfasser], and Bruno [Akademischer Betreuer] Eckhardt. "Localized transition states in many-particle systems / Jens Christian Pfeifer. Betreuer: Bruno Eckhardt." Marburg : Philipps-Universität Marburg, 2016. http://d-nb.info/1099594294/34.

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Stedman, Mark Laurence. "Ground state and finite-temperature quantum Monte Carlo simulations of many particle systems." Thesis, Imperial College London, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.391825.

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Rulands, Steffen [Verfasser], and Erwin [Akademischer Betreuer] Frey. "Heterogeneity and spatial correlations in stochastic many-particle systems / Steffen Rulands. Betreuer: Erwin Frey." München : Universitätsbibliothek der Ludwig-Maximilians-Universität, 2013. http://d-nb.info/1056876786/34.

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Hafver, Andreas. "The formalism of non-commutative quantum mechanics and its extension to many-particle systems." Thesis, Stellenbosch : University of Stellenbosch, 2010. http://hdl.handle.net/10019.1/5255.

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Thesis (MSc (Physics))--University of Stellenbosch, 2010.
ENGLISH ABSTRACT: Non-commutative quantum mechanics is a generalisation of quantum mechanics which incorporates the notion of a fundamental shortest length scale by introducing non-commuting position coordinates. Various theories of quantum gravity indicate the existence of such a shortest length scale in nature. It has furthermore been realised that certain condensed matter systems allow effective descriptions in terms of non-commuting coordinates. As a result, non-commutative quantum mechanics has received increasing attention recently. A consistent formulation and interpretation of non-commutative quantum mechanics, which unambiguously defines position measurement within the existing framework of quantum mechanics, was recently presented by Scholtz et al. This thesis builds on the latter formalism, extends it to many-particle systems and links it up with non-commutative quantum field theory via second quantisation. It is shown that interactions of particles, among themselves and with external potentials, are altered as a result of the fuzziness induced by non-commutativity. For potential scattering, generic increases are found for the differential and total scattering cross sections. Furthermore, the recovery of a scattering potential from scattering data is shown to involve a suppression of high energy contributions, disallowing divergent interaction forces. Likewise, the effective statistical interaction among fermions and bosons is modified, leading to an apparent violation of Pauli’s exclusion principle and foretelling implications for thermodynamics at high densities.
AFRIKAANSE OPSOMMING: Nie-kommutatiewe kwantummeganika is ’n veralgemening van kwantummeganika wat die idee van ’n fundamentele kortste lengteskaal invoer d.m.v. nie-kommuterende ko¨ordinate. Verskeie teorie¨e van kwantum-grawitasie dui op die bestaan van so ’n kortste lengteskaal in die natuur. Dit is verder uitgewys dat sekere gekondenseerde materie sisteme effektiewe beskrywings in terme van nie-kommuterende koordinate toelaat. Gevolglik het die veld van nie-kommutatiewe kwantummeganika onlangs toenemende aandag geniet. ’n Konsistente formulering en interpretasie van nie-kommutatiewe kwantummeganika, wat posisiemetings eenduidig binne bestaande kwantummeganika raamwerke defineer, is onlangs voorgestel deur Scholtz et al. Hierdie tesis brei uit op hierdie formalisme, veralgemeen dit tot veeldeeltjiesisteme en koppel dit aan nie-kommutatiewe kwantumveldeteorie d.m.v. tweede kwantisering. Daar word gewys dat interaksies tussen deeltjies en met eksterne potensiale verander word as gevolg van nie-kommutatiwiteit. Vir potensiale verstrooi ¨ıng verskyn generiese toenames vir die differensi¨ele and totale verstroi¨ıngskanvlak. Verder word gewys dat die herkonstruksie van ’n verstrooi¨ıngspotensiaal vanaf verstrooi¨ıngsdata ’n onderdrukking van ho¨e-energiebydrae behels, wat divergente interaksiekragte verbied. Soortgelyk word die effektiewe statistiese interaksie tussen fermione en bosone verander, wat ly tot ’n skynbare verbreking van Pauli se uitsluitingsbeginsel en dui op verdere gevolge vir termodinamika by ho¨e digthede.

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Endres, Manuel [Verfasser], and Immanuel [Akademischer Betreuer] Bloch. "Probing correlated quantum many-body systems at the single-particle level / Manuel Endres. Betreuer: Immanuel Bloch." München : Universitätsbibliothek der Ludwig-Maximilians-Universität, 2013. http://d-nb.info/1032862610/34.

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Ferreira, Marina Amado. "Congestion in many-particle systems with volume exclusion constraints : algorithms and applications to modelling in biology." Thesis, Imperial College London, 2018. http://hdl.handle.net/10044/1/62322.

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Many-particle systems with congestion are widely found in biology, for example, in cell tissues or herds. Mathematical modelling constitutes an important tool in their study. In contrast to common approaches, we propose two new modelling frameworks that rely on the exact treatment of the contacts between particles: a particle-based and a continuum framework. Both frameworks are based on the same behavioural rules, namely 1) two particles cannot overlap with each other and 2) the particles seek a minimum of a given confining potential at all times. The dynamics is driven by the evolution of the potential and changes in particle characteristics, such as size. In the first part, the static equilibria of the particle-based model are obtained as solutions to a minimization problem. This leads to non-convex optimization under volume exclusion constraints. Classical tools are either not applicable or not efficient. We develop and study a new and efficient minimization algorithm to approximate a solution. The second part concerns the time-evolution of the particle-based framework. We develop new time-stepping schemes involving the resolution of a minimization problem at each time-step, which is tackled with the minimization algorithm developed in the first part. The study of these schemes is performed in the case of a system of hard-spheres undergoing ballistic aggregation on a torus and it succeeds to simulate up to one million particles. These new tools are applied to the study of the mechanics of a cell tissue, which has allowed to validate them in practice. In the third part, we develop a continuum modelling framework describing the evolution of particle density. Our approach differs from previous ones by relying on different modelling assumptions that are more appropriate to biological systems. We show that this novel approach leads to a free-boundary problem and we characterize the dynamics of the boundary.

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Geisinger, Alissa [Verfasser], and Christian [Akademischer Betreuer] Hainzl. "Effective Models for Many Particle Systems : BCS Theory and the Kac Model / Alissa Geisinger ; Betreuer: Christian Hainzl." Tübingen : Universitätsbibliothek Tübingen, 2018. http://d-nb.info/1198973447/34.

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Fuchs, Sebastian [Verfasser], Thomas [Akademischer Betreuer] Pruschke, and Fakher [Akademischer Betreuer] Assaad. "Thermodynamic and spectral properties of quantum many-particle systems / Sebastian Fuchs. Gutachter: Thomas Pruschke ; Fakher Assaad. Betreuer: Thomas Pruschke." Göttingen : Niedersächsische Staats- und Universitätsbibliothek Göttingen, 2011. http://d-nb.info/1044360941/34.

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Schüler, Michael Verfasser], Jamal [Akademischer Betreuer] Berakdar, Ingrid [Akademischer Betreuer] [Mertig, and Robert [Akademischer Betreuer] Leeuwen. "Tracking inter-particle correlations by many-body spectroscopies from complex systems : [kumulative Dissertation] / Michael Schüler ; Jamal Berakdar, Ingrid Mertig, Robert Leeuwen." Halle, 2016. http://d-nb.info/1122438672/34.

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Schüler, Michael Verfasser], Jamal [Akademischer Betreuer] [Berakdar, Ingrid [Akademischer Betreuer] Mertig, and Robert [Akademischer Betreuer] Leeuwen. "Tracking inter-particle correlations by many-body spectroscopies from complex systems : [kumulative Dissertation] / Michael Schüler ; Jamal Berakdar, Ingrid Mertig, Robert Leeuwen." Halle, 2016. http://nbn-resolving.de/urn:nbn:de:gbv:3:4-18967.

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Winkler, Anton [Verfasser], and Erwin [Akademischer Betreuer] Frey. "Analytic approaches to stochastic many-particle systems : Scaling and renormalization in microbial communities and in chemical kinetics / Anton Winkler. Betreuer: Erwin Frey." München : Universitätsbibliothek der Ludwig-Maximilians-Universität, 2012. http://d-nb.info/1028738323/34.

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Altevogt, Torsten. "Der optische Start-Effekt mit quantisiertemStrahlungsfeld." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I, 2000. http://dx.doi.org/10.18452/14465.

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Bei der theoretischen Beschreibung von spektroskopischen Experimenten wird in der Regel das Materiesystem quantenmechanisch beschrieben, während das Strahlungsfeld klassisch behandelt wird. Diese semiklassische Näherung ist zur Beschreibung von Experimenten, bei denen eine starke Kopplung zwischen dem Matriesystem und einzelnen Photonen besteht, nicht mehr gültig. Dies kann beispielsweise innerhalb eines optischen Resonators der Fall sein. In dieser Arbeit wird am Beispiel eines Pump-Test- Experiments zum Nachweis des optischen Stark-Effekts untersucht, welche zusätzlichen Effekte sich bei einer quantisierten Beschreibung des Strahlungsfeldes ergeben. Ein signifikanter Effekt ist, dass die Photonenstatistik des Pumpfeldes sich in der Linienform der verschobenen Resonanzlinie widerspiegelt. Weiter wurde in dieser Arbeit bei kleiner Pumpverstimmung ein Verstärkungseffekt gefunden, der ebenfalls auf der quantisierten Behandlung des Strahlungsfeldes beruht (nichtklassische Verstärkung). Es treten ferner bei grosseren Ensemblen von Zwei-Niveau -Systemen zusätzliche Unterstrukturen und Resonanzen auf. Auch kann der Nachweis des optischen Stark-Effekts Aufschluss über die Nichtdiagonalelemente bezüglich der Photonenzahl des quantisierten Pumpfeldes geben.Im Hinblick auf die Beschreibung komplexer Materiesystemen wurde in dieser Arbeit auch eine näherungsweise Berechnung der Testabsorption mit quantisiertem Strahlungsfeld im Rahmen einer Dichtematrixtheorie untersucht. Insbesondere war hier für die quantitative Beschreibung der nichtklassischen Verstärkung eine Berücksichtigung hoherer Korrelationen zwingend erforderlich. Auch wurden näherungsweise Entkopp- lungen unter Berücksichtigung der Erhaltungsgrossen durch- geführt. Die Dichtematrixtheorie wurde auf die Untersuchung des optischen Stark-Effektes an storstellengebundenen Exzitonen in Halbleitern angewandt. Da diese Resonanzen vergleichsweise kleine homogene und inhomogene Linienbreiten aufweisen,ist hier experimentell zu erwarten, dass sich feine Effekte des quantisierten Pumpfeldes bemerkbar machen konnen.
The theoretical description of spectroscopic experiments usu ally relies on a semiclassical approach where the matter system is described in terms of quantum mechanics while the radiation field is treated classically. This approach does n ot work well for systems with a strong coupling between the matter system and photons of the radiation field. The latter can be the case within an optical resonator.In this thesis, additional effects of a quantized radiation field are inves tigated on a pump-probe experiment for detecting the optical Stark effect. One significant effect is that the lineshape of the shifted resonance displays the photon statistics of the pump field. For small pump detuning probe gain results in a frequency regime where the semiclassical treatment predicts absorption. This effect is refered to nonclassical gain. For larger ensembles of two-level systems, additional substructures and resonances appear within the probe absorption spectrum. Also non- diagonal elements of the field density matrix can be detected in such an experiment. In order to describe a more complex matter systems, the optical Stark effect has been treated in terms of a density matrix approach with quantized radiation fields. For a quantitative description of nonclassical gain, higher correlation terms had to be treated properly. Moreover, conserved quantities were taken into account in approximate decouplings. The density matrix approach was applied to the description of the optical Stark effect on impurity-bound excitons in semiconductors. These systems are of high interest as their narrow resonances might allow the demonstration of fine effects of the quantized radiation field.

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Carrapatoso, Kléber. "Théorèmes asymptotiques pour les équations de Boltzmann et de Landau." Phd thesis, Université Paris Dauphine - Paris IX, 2013. http://tel.archives-ouvertes.fr/tel-00920455.

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Nous nous intéressons dans cette thèse à la théorie cinétique et aux systèmes de particules dans le cadre des équations de Boltzmann et Landau. Premièrement, nous étudions la dérivation des équations cinétiques comme des limites de champ moyen des systèmes de particules, en utilisant le concept de propagation du chaos. Plus précisément, nous étudions les probabilités chaotiques sur l'espace de phase de ces systèmes de particules : la sphère de Boltzmann, qui correspond à l'espace de phase d'un système de particules qui évolue conservant le moment et l'énergie ; et la sphère de Kac, correspondant à un système de particules qui conserve seulement l'énergie. Ensuite, nous nous intéressons à la propagation du chaos, avec des estimations quantitatives et uniforme en temps, pour les équations de Boltzmann et Landau. Deuxièmement, nous étudions le comportement asymptotique en temps grand des solutions de l'équation de Landau.

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Kavalchuk, Eduard. "Perturbative calculations in many-particle systems." 2008. http://hdl.handle.net/1993/21214.

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28

"Topics in many-particle quantum systems." 2005. http://library.cuhk.edu.hk/record=b5896443.

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Abstract:

Lo Loc Ping = 多體量子系統問題 / 盧樂平.
Thesis submitted in: October 2004.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2005.
Includes bibliographical references (leaves 168-171).
Text in English; abstracts in English and Chinese.
Lo Loc Ping = Duo ti liang zi xi tong wen ti / Lu Leping.
Abstract --- p.i
摘要 --- p.ii
Acknowledgment --- p.iii
Chapter I --- Computational Quantum Mechanics and Its Applications 電算量子力學及其應用 --- p.1
Chapter 1 --- An Overview of Quantum Mechanics and Some Important Tools of Theory --- p.2
Chapter 1.1 --- The Schrodinger Equation --- p.2
Chapter 1.2 --- The Variational Method --- p.4
Chapter 1.2.1 --- Rayleigh-Ritz Approach --- p.4
Chapter 1.2.2 --- Linear Variation --- p.5
Chapter 2 --- Theoretical Methodology of Electronic Structures: Ab Initio Molecular Orbital Theory --- p.7
Chapter 2.1 --- The Molecular Hamiltonian --- p.7
Chapter 2.2 --- Hartree Description and Linear Combination of Atomic Orbitals Expan- sion --- p.8
Chapter 2.3 --- Slater Determinant and the Pauli Exclusion Principle --- p.9
Chapter 2.4 --- The Expansion of E in Terms of Integrals over MOs --- p.11
Chapter 2.5 --- Derivation of the Hartree´ؤFock Equations --- p.15
Chapter 2.6 --- The Self-Consistent Field Calculation --- p.18
Chapter 2.7 --- Koopmans' Theorem --- p.19
Chapter 2.8 --- Orbital and the Total SCF Electronic Energy --- p.20
Chapter 2.9 --- AO Basic Sets --- p.21
Chapter 2.9.1 --- Slater-Type Orbitals --- p.21
Chapter 2.9.2 --- Gaussian Functions --- p.22
Chapter 2.10 --- The Hartree-Fock Limit --- p.23
Chapter 2.11 --- Electron Correlation --- p.23
Chapter 2.11.1 --- Weakness in the Single Determinant Model --- p.23
Chapter 2.11.2 --- Configuration Interaction --- p.24
Chapter 2.11.3 --- The Coupled-Cluster Method --- p.25
Chapter 2.11.4 --- Density Functional Theory --- p.26
Chapter 2.12 --- Frontier Orbitals --- p.31
Chapter 3 --- Theoretical Investigation of the Interaction between Metal and Tris(8- hydroxyquinoline) aluminum in Organic Light Emitting Diodes --- p.32
Chapter 3.1 --- Organic Light Emitting Diodes and Tris(8-hydro-xyquinoline) aluminum --- p.32
Chapter 3.2 --- Computational Methodology --- p.33
Chapter 3.3 --- Alq3 --- p.34
Chapter 3.3.1 --- Molecular Structure --- p.34
Chapter 3.3.2 --- Electronic Structure --- p.36
Chapter 3.3.3 --- Transition and Relaxation Energies --- p.44
Chapter 3.3.4 --- Interactions with Metals --- p.45
Chapter 3.4 --- "Li-Alq3, Na-Alq3 and K-Alq3 Complexes" --- p.46
Chapter 3.4.1 --- Molecular Structure --- p.46
Chapter 3.4.2 --- Ground-State Electronic Structure --- p.55
Chapter 3.4.3 --- Transition and Relaxation Energies --- p.67
Chapter 3.5 --- "Be-Alq3, Mg´ؤAlq3 and Ca´ؤAlq3 Complexes" --- p.68
Chapter 3.5.1 --- Molecular Structure --- p.68
Chapter 3.5.2 --- Ground-State Electronic Structure --- p.76
Chapter 3.5.3 --- Transition and Relaxation Energies --- p.87
Chapter 3.6 --- "B-Alq3, Al-Alq3 and Ga-Alq3 Complexes" --- p.87
Chapter 3.6.1 --- Molecular Structure --- p.87
Chapter 3.6.2 --- Ground-State Electronic Structure --- p.95
Chapter 3.6.3 --- Transition and Relaxation Energies --- p.106
Chapter II --- Analytical Studies of Polarons and the Electron-Phonon Interaction 極子與電子一聲子相互作用的解析研究 --- p.107
Chapter 4 --- Optimal Coupled-Cluster Approximation of the Ground-State Energy of the E× (α1 + α1) Jahn-Teller System --- p.108
Chapter 4.1 --- The Jahn-Teller Effect --- p.108
Chapter 4.2 --- Approximation in the Coupled-Cluster Method and the Jahn-Teller Hamiltonian --- p.110
Chapter 4.3 --- Variational Coupled-Cluster Approximation --- p.112
Chapter 4.3.1 --- The Zeroth Level --- p.113
Chapter 4.3.2 --- The First Level --- p.113
Chapter 4.3.3 --- The Second and the Third Levels --- p.114
Chapter 4.4 --- An 'Optimal' Hamiltonian --- p.115
Chapter 4.5 --- Treatment for the k> 1 Case --- p.117
Chapter 4.6 --- Energies and Other Physical Phenomena --- p.118
Chapter 5 --- Small-to-Large Ground-State Polaron Crossover in One-Dimension Extended E×e Jahn-Teller System Using Variational Coupled-Cluster Approximation --- p.134
Chapter 5.1 --- Polaron Formation --- p.134
Chapter 5.2 --- Model Hamiltonian and the MLF Transformation --- p.135
Chapter 5.3 --- Variatonal Coupled-Cluster Approximation --- p.137
Chapter 5.3.1 --- Zeorth Level --- p.139
Chapter 5.3.2 --- First Level --- p.139
Chapter 5.3.3 --- Second Level --- p.142
Chapter 5.4 --- Energies and Static Correlation Functions --- p.142
Chapter 5.5 --- Approximate Form of the MLF Transformation for K = 0 --- p.153
Chapter 5.5.1 --- Zeroth Level --- p.154
Chapter 5.5.2 --- First Level --- p.155
Chapter 5.5.3 --- Second Level --- p.156
Chapter 5.5.4 --- Energies and Static Correlation Functions --- p.157
Chapter 5.6 --- Synopsis --- p.167
Bibliography --- p.171

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29

"Topics in many-particle quantum systems." 2007. http://library.cuhk.edu.hk/record=b5893502.

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Abstract:

Li, Kwan Ho = 多體量子系統問題 / 李君豪.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2007.
Includes bibliographical references (leaves [243]-246).
Text in English; abstracts in English and Chinese.
Li, Kwan Ho = Duo ti liang zi xi tong wen ti / Li Junhao.
Abstract --- p.i
Acknowledgment --- p.iv
Chapter I --- Computational Quantum Mechanics and Its Applications --- p.1
Chapter 1 --- Theoretical Methodology of Electronic Structures --- p.2
Chapter 1.1 --- The Schrodinger Equation --- p.3
Chapter 1.2 --- Molecular Hamiltonian and Born-Oppenheimer Approximation --- p.4
Chapter 1.3 --- The Variational Method --- p.7
Chapter 1.3.1 --- Rayleigh-Ritz Variation Principle --- p.7
Chapter 1.3.2 --- Linear Variation --- p.8
Chapter 1.4 --- Many-Electron Wavfunction --- p.9
Chapter 1.4.1 --- Hartree-product Wavefunction --- p.9
Chapter 1.4.2 --- Slater Determinant and the Pauli Exclusion Principle --- p.11
Chapter 1.5 --- The Expectation Value of Total Electronic Energy --- p.13
Chapter 1.6 --- Derivation of the Hartree-Fock Equations --- p.16
Chapter 1.7 --- Orbital Energies and the SCF Total Electronic Energy --- p.19
Chapter 1.8 --- Koopmans' Theorem --- p.20
Chapter 1.9 --- The LCAO expansion and Self-Consistent Field Calculation --- p.22
Chapter 1.10 --- AO Basis Sets --- p.23
Chapter 1.10.1 --- Slater-Type Orbitals --- p.24
Chapter 1.10.2 --- Gaussian Functions --- p.24
Chapter 1.11 --- Hartree-Fock Limit --- p.25
Chapter 1.12 --- Electron Correlation --- p.26
Chapter 1.12.1 --- Weakness in the Single Determinantal Wavefunction --- p.26
Chapter 1.12.2 --- Configuration Interaction --- p.26
Chapter 1.13 --- Density Functional Theory --- p.27
Chapter 1.13.1 --- Early approximations --- p.28
Chapter 1.13.2 --- Hohenberg-Kohn Theorems --- p.31
Chapter 1.13.3 --- Kohn-Sham (KS) Method --- p.33
Chapter 1.13.4 --- Exchange-Correlation Energy Functional and B3LYP --- p.36
Chapter 2 --- Theoretical Investigation of Oxadiazole-Triphenylamine Based Compounds --- p.40
Chapter 2.1 --- Organic Light Emitting Diode and Oxadiazole-Triphenylamine Based Com- pounds --- p.40
Chapter 2.2 --- Methodology --- p.42
Chapter 2.2.1 --- Theoretical Methodology --- p.42
Chapter 2.2.2 --- Computational Methodology --- p.46
Chapter 2.3 --- Computational Results --- p.47
Chapter 2.3.1 --- Molecular Structure --- p.47
Chapter 2.3.2 --- Electronic Structure --- p.79
Chapter 2.4 --- Absorption and Emission Energy --- p.94
Chapter 2.5 --- Reorganization Energy and Mobility --- p.95
Chapter 2.6 --- Summary --- p.99
Chapter 3 --- The Transport Properties of Oligoacenes --- p.102
Chapter 3.1 --- Introduction --- p.102
Chapter 3.2 --- Computational Details --- p.103
Chapter 3.3 --- Results and Discussions --- p.103
Chapter 3.3.1 --- Molecular Configuration --- p.103
Chapter 3.3.2 --- Reorganization Energy --- p.106
Chapter 3.3.3 --- Coupling Matrix Element --- p.107
Chapter 3.4 --- Conclusion --- p.133
Chapter 4 --- The Transport Properties in Rubrene Thin Film and Crystal --- p.135
Chapter 4.1 --- Introduction --- p.135
Chapter 4.2 --- Computational Details --- p.137
Chapter 4.3 --- Results and Discussions --- p.137
Chapter 4.3.1 --- Molecular Structure --- p.137
Chapter 4.3.2 --- Frontier Orbitals --- p.144
Chapter 4.3.3 --- Reorganization Energy --- p.147
Chapter 4.3.4 --- Coupling Matrix Element and Mobility --- p.147
Chapter 4.4 --- Conclusion --- p.175
Chapter II --- Analytical Studies of Anisotropic Spin-1/2 Heisenberg Anti-ferromagnetic Linear Chains --- p.177
Chapter 5 --- Coupled-Cluster Approximation for Two Anisotropic Spin-1/2 Heisenberg Antiferromagnetic Linear Chains with Inter-chain Anisotropic Ferromagnetic Interaction --- p.178
Chapter 5.1 --- Introduction --- p.178
Chapter 5.2 --- Approximation in the Coupled-Cluster Method --- p.179
Chapter 5.3 --- Anisotropic spin-1/2 Heisenberg Antiferromagnetic Model in One Dimension --- p.183
Chapter 5.3.1 --- The Zeroth Level --- p.185
Chapter 5.3.2 --- The First Level --- p.186
Chapter 5.3.3 --- The Second Level --- p.189
Chapter 5.4 --- Two Anisotropic Spin-1/2 Heisenberg Antiferromagnetic Linear Chains with Inter-chain Anisotropic Ferromagnetic Interaction --- p.198
Chapter 5.4.1 --- The Zeroth Level --- p.199
Chapter 5.4.2 --- The First Level --- p.201
Chapter 5.4.3 --- The Second Level --- p.206
Chapter 5.5 --- Conclusion --- p.242
Bibliography --- p.243

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30

"Topics on many-particle quantum systems." 2006. http://library.cuhk.edu.hk/record=b5892853.

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Abstract:

Yeung Man Yi = 多體量子系統問題 / 楊曼儀.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2006.
Includes bibliographical references (leaves [247-249]).
Text in English; abstracts in English and Chinese.
Yeung Man Yi = Duo ti liang zi xi tong wen ti / Yang Manyi.
Abstract --- p.i
Acknowledgment --- p.iii
Chapter I --- Computational Quantum Mechanics and Its Applications
電算量子力學及其應用 --- p.1
Chapter 1 --- Theoretical Methodology of Electronic Structures: Ab Initio Molecular Orbital Theory --- p.2
Chapter 1.1 --- Molecular Hamiltonian --- p.2
Chapter 1.2 --- Hartree Products --- p.5
Chapter 1.3 --- Slater Determinants and Pauli Exclusion Principle --- p.6
Chapter 1.4 --- Expansion of Total Electronic Energy in terms of Integrals over MOs --- p.8
Chapter 1.5 --- Derivation of the Hartree-Fock Equations --- p.11
Chapter 1.6 --- Orbital Energies and the Koopmans' Theorem --- p.14
Chapter 1.7 --- AO Basic Sets --- p.17
Chapter 1.7.1 --- Slater-Type Orbitals --- p.18
Chapter 1.7.2 --- Gaussian Functions --- p.18
Chapter 1.8 --- Self-Consistent Field Calculation --- p.19
Chapter 1.9 --- Hartree-Fock Limit --- p.20
Chapter 1.10 --- Electron Correlation --- p.20
Chapter 1.10.1 --- Configuration Interaction --- p.20
Chapter 1.10.2 --- Density Functional Theory --- p.21
Chapter 2 --- Theoretical Investigation of Organic Light Emitting Molecules --- p.29
Chapter 2.1 --- Introduction --- p.29
Chapter 2.2 --- Methodology --- p.31
Chapter 2.2.1 --- Theoretical Methodology --- p.31
Chapter 2.2.2 --- Computational Methodology --- p.35
Chapter 2.3 --- ADN series --- p.35
Chapter 2.3.1 --- Molecular Structure --- p.36
Chapter 2.3.2 --- Electronic Structure --- p.49
Chapter 2.3.3 --- Absorption and Emission Energy --- p.55
Chapter 2.3.4 --- Reorganization Energy --- p.56
Chapter 2.3.5 --- Mobility --- p.57
Chapter 2.3.6 --- Summary on ADN series --- p.66
Chapter 2.4 --- XOT series --- p.67
Chapter 2.4.1 --- Molecular Structure --- p.68
Chapter 2.4.2 --- Electronic Structure --- p.89
Chapter 2.4.3 --- Absorption and Emission Energy --- p.96
Chapter 2.4.4 --- Reorganization Energy and Mobility --- p.98
Chapter 2.4.5 --- Summary on XOT series --- p.100
Chapter 2.5 --- KPA series --- p.102
Chapter 2.5.1 --- Molecular Structure --- p.102
Chapter 2.5.2 --- Electronic Structure --- p.123
Chapter 2.5.3 --- Absorption and Emission Energy --- p.131
Chapter 2.5.4 --- Reorganization Energy and Mobility --- p.131
Chapter 2.5.5 --- Summary on KPA series --- p.133
Chapter 2.6 --- NPA series --- p.136
Chapter 2.6.1 --- Molecular Structure --- p.136
Chapter 2.6.2 --- Electronic Structure --- p.160
Chapter 2.6.3 --- Absorption and Emission Energy --- p.166
Chapter 2.6.4 --- Reorganization Energy and Mobility --- p.167
Chapter 2.6.5 --- Summary on NPA series --- p.169
Chapter II --- Analytical Studies of Polarons and the Electron-Phonon Interaction
極子與電子一聲子相互作用的解析研究 --- p.172
Chapter 3 --- Study on Holstein Model Using Variational Approximation --- p.173
Chapter 3.1 --- Holstein Hamiltonian --- p.173
Chapter 3.2 --- Variational Transformation --- p.175
Chapter 3.2.1 --- Lang-Firsov Transformation --- p.175
Chapter 3.2.2 --- Squeezing Transformation --- p.177
Chapter 3.3 --- Energy and Static Correlation Functions --- p.179
Chapter 4 --- Study on Holstein Model Using Coupled-Cluster Method --- p.193
Chapter 4.1 --- Approximation in the Coupled-Cluster Method --- p.193
Chapter 4.2 --- Approach 1 --- p.195
Chapter 4.2.1 --- The Zeroth and the First Levels --- p.195
Chapter 4.2.2 --- Energies and Static Correlation Functions --- p.196
Chapter 4.3 --- Approach 2 --- p.206
Chapter 4.3.1 --- The Zeroth and the First Levels --- p.206
Chapter 4.3.2 --- Energies and Static Correlation Functions --- p.210
Chapter 4.4 --- Approach 3 --- p.225
Chapter 4.4.1 --- The Zeroth and the First Levels --- p.226
Chapter 4.4.2 --- Energies and Static Correlation Functions --- p.228
Chapter 4.5 --- Comparison with the Variational Method --- p.243

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31

Zhu, Siyu. "Particle Dynamics Simulation toward High-Shear Mixing Process in Many Particle Systems." Thesis, 2018. https://doi.org/10.7916/D89G74QC.

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Granular materials appear in a broad range of industrial processes, including mineral processing, plastics manufacturing, ceramic component, pharmaceutical tablets and food products. Engineers and scientists are always seeking efficient tools that can characterize, predict, or simulate the effective material properties in a timely manner and with acceptable accuracy, such that the cost for design and develop novel composite granular materials could be reduced. The major scope of this dissertation covers the development, verification and validation of particle system simulations, including solid-liquid two-phase particle mixing process and foaming asphalt process. High shear mixing process is investigated in detail with different types of mixers. Besides particle mixing study, one liquid-gas two phase foaming asphalt simulation is studied to show the broad capacity of our particulate dynamics simulation scheme. Methodologies and numerical studies for different scenarios are presented, and acceleration plans to speed up the simulations are discussed in detail. The dissertation starts with the problem statement, which briefly demonstrates the background of the problem and introduces the numerical models built from the physical world. In this work, liquid-solid two-phase particle mixing process is mainly studied. These mixing processes are conducted in a sealed mixer and different types of particles are mixed with the rotation of the mixer blades, to obtain a homogeneous particle mixture. In addition to the solid-liquid particle mixing problem, foaming asphalt problem, which is a liquid-gas two phase flow problem is also investigated. Foaming asphalt is generated by injecting a small amount of liquid additive (usually water) to asphalt at a high temperature. The volume change during this asphalt foaming process is studied. Given the problem statement, detailed methodologies of particle dynamics simulation are illustrated. For solid-liquid particle mixing, Smoothed Particle Hydrodynamics (SPH) and Discrete Element Method (DEM) are introduced and implemented to simulate the dynamics of solid and liquid particles, respectively. Solid-liquid particle interactions are computed according to Darcy`s Law. Then the proposed SPH coupling DEM model is verified by three classical case studies. For foaming asphalt problems, a SPH numerical model for foaming asphalt simulation is proposed, and simulations with different water contents, pressures and temperatures are conducted and the results agree with the experiments well. The coupled SPH-DEM method is applied to the particle mixing process, and several particle mixing numerical studies are conducted and these simulations are analyzed in multiple aspects. For the solid-liquid particle mixing problem, liquid plays an important role in the mixing performance. The effects of liquid content and liquid viscosity on mixing performance are studied. The mixing indexes of the mixture are applied to analyze the mixing quality, and the differences between three kinds of mixing indexes are discussed. Then mixers commonly used in industry such as Double Planetary Mixer (DPM) are modeled in mixing simulation and their results are compared with the experiments. Similar to other numerical simulation problems, the scale of the model and the accuracy of the simulation results are constrained by the computational capacity. Our in-house software package Particle Dynamics Parallel Simulator(PDPS) has been used as a platform to implement the algorithms above and conduct the simulations. Two parallel computing methods of Message Passing Interface (MPI) parallel computing and Graphics Processing Unit (GPU) acceleration have been used to accelerate the simulations. Speedup results for both MPI parallel computing and GPU methods are illustrated in the case studies. In summary, a comprehensive approach for particle simulation is proposed and applied to particle mixing process and asphalt foaming simulation. The simulation results are analyzed in various aspects to provide valuable insights to the problems studied in this work. Given the improvement of computational capacity, particle dynamics in higher resolution and simulations in more complex configurations can be obtained. This particle simulation platform is general and it can be straightforwardly extended to many-particle systems with more particle phases and solid-liquid-gas dynamics problems.

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32

Fuchs, Sebastian. "Thermodynamic and spectral properties of quantum many-particle systems." Doctoral thesis, 2011. http://hdl.handle.net/11858/00-1735-0000-0006-B4E9-D.

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33

Dufresne, Eric Robert. "Hydrodynamic coupling and optical patterning of many-particle colloidal systems /." 2000. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:9977999.

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34

Dammer, Stephan M. [Verfasser]. "Stochastic many-particle systems with irreversible dynamics / von Stephan M. Dammer." 2004. http://d-nb.info/974953334/34.

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35

Hsiuan, Chen Chi, and 陳濟鉉. "A study of fast multipole algorithm for many-particle interacting systems." Thesis, 2001. http://ndltd.ncl.edu.tw/handle/25201735543710492396.

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36

Ku, Wei. "Electronic excitations in metals and semiconductors : Ab Initio studies of realistic many-particle systems /." 2000. http://etd.utk.edu/2000/KuWei.pdf.

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37

Verma, Anurag. "Modeling the free energy functional at the fluid-solid transition in classical many-particle systems." 2012. https://scholarworks.umass.edu/dissertations/AAI3498373.

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The problem of phase equilibrium in colloidal and classical atomistic systems is of great interest in modern micro/nano fabrication and self-assembly processes. Systems with specific potential interactions are increasingly being developed and knowledge of their phase diagrams would aid in their use in materials applications. The conventional methods of using simulations and experiments to evaluate phase equilibrium are costly, especially for fluid-solid equilibrium. One way to address this problem is to improve the accuracy of theories, such as classical density functional theory (cDFT), that predict thermodynamic properties at the fluid-solid transition with modest computational cost. In such a program the challenges are of two kinds, viz. (1) the development of a new cDFT formulation to treat fluid-solid equilibrium, especially with regard to the higher order multi-body interaction terms in the free energy expression and (2) finding a more accurate numerical method to solve the cDFT equations. In our work we develop several numerical and inversion methodologies to meet these challenges, including closure relations that capture the higher order terms in the free energy expansion. We find that these closures are qualitatively and quantitatively very different from their liquid state analogs found in the Ornstein-Zernike integral equation theory. Specifically, we discover new closure relations applicable to the fluid-solid transition in hard-sphere, soft-repulsive and Lennard-Jones potentials. We further discuss the universal nature of these closures for different interaction potentials and explore the breadth of their applicability and future prospects.

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38

Willmann, Richard Daniel [Verfasser]. "Stochastic many particle systems far from equilibrium coupled to bulk reservoirs / vorgelegt von Richard Daniel Willmann." 2004. http://d-nb.info/972173390/34.

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39

Barthel, Thomas [Verfasser]. "Entanglement entropy in quantum many-particle systems and their simulation via ansatz states / vorgelegt von Thomas Barthel." 2009. http://d-nb.info/1000891194/34.

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40

Tiegel, Alexander Clemens. "Finite-temperature dynamics of low-dimensional quantum systems with DMRG methods." Doctoral thesis, 2016. http://hdl.handle.net/11858/00-1735-0000-0028-8801-A.

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Dissertations / Theses on the topic 'Many-particle system'

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