The dynamics of demand responsive ride pooling (DRRP) systems is considered in a mean-field framework. The relevant dimensionless quantities determining the performance and viability of the system are identified. In the presence of an already established dominant market participant with comparable service quality (like, e.g., the private car), the mutual interaction of the actors (i.e., the customers sharing rides) by virtue of the route assignment algorithm gives rise to a discontinuous transition between two strongly different modes of operation. One of them represents the typical (unfavorable) performance of current ride pooling systems, while the other represents a new mode of operation in which virtually all customers use DRRP.

Agent-based asset exchange models serve as an interesting and tractable means by which to study the emergence of an economy's wealth distribution. Although asset exchange models have reproduced certain features of real-world wealth distributions, previous research has largely neglected the effects of economic growth and network connectivity between agents. In this work, we study the effects of globalization on wealth inequality in the Growth, Exchange, and Distribution (GED) model [Liu et al, Klein et al] on a network or lattice that connects potential trading partners. We find that increasing the number of trading partners per agent results in higher levels of wealth inequality as measured by the Gini coefficient and the variance of the agent wealth distribution. However, if globalization is accompanied by a proportionate increase in the economic growth rate, the level of inequality can be held constant. We present a mean-field theory to describe the GED model based on the Fokker-Planck equation and derive the stationary wealth distributions of the network GED model. For large Ginzburg parameter for which mean-field theory is applicable, the wealth distributions for the fully connected model are found to be Gaussian; however, for sparse trade networks, a non-Gaussian "hyperequal" phase is found even for large Ginzburg parameter. It is shown that several networks (Erdos-Renyi, Barabsi-Albert, one-dimensional and two-dimensional lattices) display mean-field critical exponents when the Ginzburg parameter is large and held constant and the system parameters are scaled properly.

This thesis focuses on developing new approaches to solving the ground state properties of quantum many-body Hamiltonians, and the goal is to develop a systematic approach which properly balances efficiency and accuracy. Two new formalisms are proposed in this thesis: the Variational Discrete Action Theory (VDAT) and the Off-Shell Effective Energy Theory (OET). The VDAT exploits the advantages of both variational wavefunctions and many-body Green's functions for solving quantum Hamiltonians. VDAT consists of two central components: the Sequential Product Density matrix (SPD) and the Discrete Action associated with the SPD. The SPD is a variational ansatz inspired by the Trotter decomposition and characterized by an integer N, and N controls the balance of accuracy and cost; monotonically converging to the exact solution for N → ∞. The Discrete Action emerges by treating the each projector in the SPD as an effective discrete time evolution. We generalize the path integral to our discrete formalism, which converts a dynamic correlation function to a static correlation function in a compound space. We also generalize the usual many-body Green's function formalism, which results in analogous but distinct mathematical structures due to the non-abelian nature of the SPD, yielding discrete versions of the generating functional, Dyson equation, and Bethe-Salpeter equation. We apply VDAT to two canonical models of interacting electrons: the Anderson impurity model (AIM) and the Hubbard model. We prove that the SPD can be exactly evaluated in the AIM, and demonstrate that N=3 provides a robust description of the exact results with a relatively negligible cost. For the Hubbard model, we introduce the local self-consistent approximation (LSA), which is the analogue of the dynamical mean-field theory, and prove that LSA exactly evaluates VDAT for d=∞. Furthermore, VDAT within the LSA at N=2 exactly recovers the Gutzwiller approximation (GA), and therefore N>2 provides a new class of theories which balance efficiency and accuracy. For the d=∞ Hubbard model, we evaluate N=2-4 and show that N=3 provides a truly minimal yet precise description of Mott physics with a cost similar to the GA. VDAT provides a flexible scheme for studying quantum Hamiltonians, competing both with state-of-the-art methods and simple, efficient approaches all within a single framework. VDAT will have broad applications in condensed matter and materials physics. In the second part of the thesis, we propose a different formalism, off-shell effective energy theory (OET), which combines the variational principle and effective energy theory, providing a ground state description of a quantum many-body Hamiltonian. The OET is based on a partitioning of the Hamiltonian and a corresponding density matrix ansatz constructed from an off-shell extension of the equilibrium density matrix; and there are dual realizations based on a given partitioning. To approximate OET, we introduce the central point expansion (CPE), which is an expansion of the density matrix ansatz, and we renormalize the CPE using a standard expansion of the ground state energy. We showcase the OET for the one band Hubbard model in d=1, 2, and ∞, using a partitioning between kinetic and potential energy, yielding two realizations denoted as K and X. OET shows favorable agreement with exact or state-of-the-art results over all parameter space, and has a negligible computational cost. Physically, K describes the Fermi liquid, while X gives an analogous description of both the Luttinger liquid and the Mott insulator. Our approach should find broad applicability in lattice model Hamiltonians, in addition to real materials systems. The VDAT can immediately be applied to generic quantum models, and in some cases will rival the best existing theories, allowing the discovery of new physics in strongly correlated electron scenarios. Alternatively, the OET provides a practical formalism for encapsulating the complex physics of some model and allowing extrapolation over all phase space. Both of the formalisms should find broad applications in both model Hamiltonians and real materials.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第18062号 / 理博第3940号 / 新制||理||1568(附属図書館) / 30920 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 川上 則雄, 教授 石田 憲二, 准教授 藤本 聡 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

In this thesis, Density Functional Theory (DFT) and Dynamical Mean-Field Theory (DMFT) approaches are applied to study the magnetic properties of transition metal nanosystems of different sizes and compositions. In particular, in order to take into account dynamical electron correlation effects (time-resolved local charge interactions), we have adopted the DFT+DMFT formalism and made it suitable for application to nanostructures. Preliminary application of this DFT+DMFT approach, using available codes, to study the magnetic properties of small (2 to 5-atom) Fe and FePt clusters provide meaningful results: dynamical effects lead to a reduction of the cluster magnetic moment as compared to that obtained from DFT or DFT+U (U being the Coulomb repulsion parameter). We have subsequently developed our own nanoDFT+DMFT code and applied it to examine the magnetization of iron particles containing10-147 atoms. Our results for the cluster magnetic moments are in a good agreement with experimental data. In particular, we are able to reproduce the oscillations in magnetic moment with size as observed in the experiments. Also, DFT+DMFT does not lead to an overestimation of magnetization for the clusters in the size range of 10-27 atoms found with DFT and DFT+U. On application of the nanoDFT+DMFT approach to systems with mixed geometry – Fe2O3 film, which are periodic (infinitely extended), in two directions, and finite in the third. Similar to DFT+U, we find that the surface atom magnetic moments are smaller compared to the bulk. However, the absolute values of the surface atoms magnetic moments are smaller in DFT+DMFT. In parallel, we have carried out a systematic study of magnetic anisotropy in bimetallic L10 FePt nanoparticles (20-484 atoms) by using two DFT-based approaches: direct and the torque method. We find that the magnetocrystalline anisotropy (MCA) of FePt clusters is larger than that of the pure Fe and Pt ones. We explain this effect by a large hybridization of 3d Fe- and 5d Pt-atom orbitals, which lead to enhancement of the magnetic moment of the Pt atom, and hence to a larger magnetic anisotropy because of large spin-orbit coupling of Pt atoms. In addition, we find that particles whose (large) central layer consists of Pt atoms, rather than Fe, have larger MCA due to stronger hybridization effects. Such 'protected' MCA, which does not require protective cladding, can be used in modern magnetic technologies.

Mesoporous materials are being widely used in the chemical industry in various environmentally friendly separation processes and as catalysts. Our research can be broadly described as an effort to understand the behavior of fluids confined in such materials. More specifically we try to understand the influence of state variables like temperature and pore variables like size, shape, connectivity and structural heterogeneity on both the dynamic and equilibrium behavior of confined fluids. The dynamic processes associated with the approach to equilibrium are largely unexplored. It is important to look into the dynamic behavior for two reasons. First, confined fluids experience enhanced metastabilities and large equilibration times in certain classes of mesoporous materials, and the approach to the metastable/stable equilibrium is of tremendous interest. Secondly, understanding the transport resistances in a microscopic scale will help better engineer heterogeneous catalysts and separation processes. Here we present some of our preliminary studies on dynamics of fluids in ideal pore geometries. The tool that we have used extensively to investigate the relaxation dynamics of fluids in pores is the dynamic mean field theory (DMFT) as developed by Monson[P. A. Monson, J. Chem. Phys., 128, 084701 (2008) ]. The theory is based on a lattice gas model of the system and can be viewed as a highly computationally efficient approximation to the dynamics averaged over an ensemble of Kawasaki dynamics Monte Carlo trajectories of the system. It provides a theory of the dynamics of the system consistent with the thermodynamics in mean field theory. The nucleation mechanisms associated with confined fluid phase transitions are emergent features in the calculations. We begin by describing the details of the theory and then present several applications of DMFT. First we present applications to three model pore networks (a) a network of slit pores with a single pore width; (b) a network of slit pores with two pore widths arranged in intersecting channels with a single pore width in each channel; (c) a network of slit pores with two pore widths forming an array of ink-bottles. The results illustrate the effects of pore connectivity upon the dynamics of vapor liquid phase transformations as well as on the mass transfer resistances to equilibration. We then present an application to a case where the solid-fluid interactions lead to partial wetting on a planar surface. The pore filling process in such systems features an asymmetric density distribution where a liquid droplet appears on one of the walls. We also present studies on systems where there is partial drying or drying associated with weakly attractive or repulsive interactions between the fluid and the pore walls. We describe the symmetries exhibited by the lattice model between pore filling for wetting states and pore emptying for drying states, for both the thermodynamics and dynamics. We then present an extension of DMFT to mixtures and present some examples that illustrate the utility of the approach. Finally we present an assessment the accuracy of the DMFT through comparisons with a higher order approximation based on the path probability method as well as Kawasaki dynamics.

No description available.

Anharmonic lattice dynamics and electron-phonon interactions are crucial to many intriguing physical phenomena in condensed matter physics. In my thesis, I develop theoretical methods and use them to characterize physical properties of model systems and realistic novel materials. First, I introduce vibrational dynamical mean-field theory on models of anharmonic phonons using various impurity solvers, and describe the theoretical extensions to treat non-local interactions. Second, I characterize phononic and excitonic ground state properties of the superatomic semiconductor, Re₆Se₈Cl₂, which exhibits quasi-ballistic exciton dynamics at room temperature. We attribute this behavior to the formation of polarons due to coupling with acoustic phonons and parameterize a Hamiltonian to study the ground state properties. Finally, I introduce a method to calculate the Green’s function that characterizes the equilibrium dynamical properties of polarons. I demonstrate its performance on the Holstein model at finite temperature, and show its applications to systems with general coupling, electron-electron interaction, and anharmonicity.

Orientador: Eduardo Miranda / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-23T18:51:04Z (GMT). No. of bitstreams: 1 SuarezVillagran_MarthaYolima_D.pdf: 7321255 bytes, checksum: d76479a0e0c1143207cb4ee380a8034d (MD5) Previous issue date: 2013 / Resumo: Estudamos nesta tese alguns aspectos da transição metal-isolante de Mott no caso desordenado. O modelo no qual baseamos nosso estudo é o modelo de Hubbard desordenado, que é o modelo mais simples a apresentar a transição metal-isolante de Mott. Analisamos esse modelo através da Teoria Dinâmica de Campo Médio Estatística (StatDMFT). Essa teoria é uma extensão natural da Teoria Dinâmica de Campo Médio (DMFT), que foi usada com relativo sucesso nos últimos anos para analisar a transição de Mott no caso limpo. Como no caso dessa última, a StatDMFT incorpora os efeitos de correlação eletrônica apenas nos seus aspetos locais. A desordem é tratada de maneira a incorporar todos os efeitos de localização de Anderson. Com essa técnica, analisamos a transição de Mott desordenada no caso bi-dimensional, usando o Monte Carlo quântico para resolver os problemas de impureza única de Anderson requeridos pela StatDMFT. Encontramos as linhas espinodais nas quais o metal e o isolante deixam de ser meta-estáveis. Também estudamos os padrões espaciais das flutuações de quantidades locais, como a auto-energia e a função de Green local, e mostramos como há o aparecimento de regiões metálicas dentro do isolante e viceversa. Analisamos efeitos de tamanho finito e mostramos que, em consonância com os teoremas de Imry e Ma, a transição de primeira ordem desaparece no limite termodinâmico. Analisamos as propriedades de transporte desse sistema através de um mapeamento a um sistema de resistores aleatórios clássicos e calculamos a corrente média e sua distribuição através da transição metal-isolante. Finalmente, estudamos o comportamento da parede de domínio que se forma entre o isolante e o metal no caso limpo. Isso foi feito através de um modelo de uma cadeia unidimensional conectada a reservatórios, um metálico e um isolante, cada um em uma de suas extremidades. Nesse caso, utilizamos o método da Teoria de Perturbação Iterada para a solução dos modelos de impureza única. Encontramos o comportamento da parede como função da temperatura e das interações / Abstract: In this thesis, we studied some aspects of the Mott metal-insulator transition in the disordered case. The model on which we based our analysis is the disordered Hubbard model, which is the simplest model capable of capturing the Mott metal-insulator transition. We investigated this model through the Statistical Dynamical Mean-Field Theory (statDMFT). This theory is a natural extension of the Dynamical Mean-Field Theory (DMFT), which has been used with relative success in the last several years with the purpose of describing the Mott transition in the clean case. As is the case for the latter theory, the statDMFT incorporates the electronic correlation effects only incorporate Anderson localization effects.. With this technique, we analyzed the disordered two-dimensional Mott transition, using Quantum Monte Carlo to solve the associated single-impurity problems. We found the spinodal lines at which metal and insulator cease to be meta-stable. We also studied the spatial fluctuations of local quantities, such as the self-energy and the local Green¿s function, and showed the appearance of metallic regions within the insulator and vice-versa. We carried out an analysis of finite-size effects and showed that, in agreement with the theorems of Imry and Ma, the first-order transition is smeared in the thermodynamic limit. We analyzed transport properties by means of a mapping to a random classical resistor network and calculated both the average current and its distribution across the metalinsulator transition. Finally, we studied the behavior of the domain wall which forms between the metal and the insulator in the clean case. This was done by means of a model of a one-dimensional chain connected to two reservoirs, one metallic and the other insulating, each attached to one of the chain¿s ends. In this case, we used the Iterated Perturbation Theory technique in order to solve the associated singleimpurity problems. We then established the behavior of the domain wall width as a function of temperature and interactions / Doutorado / Física / Doutora em Ciências

Thesis (MSc (Physics))--Stellenbosch University, 2008. / Nuclear physics can be applied in various ways to the study of neutron stars. This thesis reports on one such application, where the relativistic mean-field approximation has been employed to calculate the equations of state of matter in the neutron star interior. In particular the equations of state of nuclear and neutron star matter of the NL3, PK1 and FSUGold parameter sets were derived. A survey of available literature on neutron stars is presented and we use the derived equations of state to reproduce the properties of saturated nuclear matter as well as the mass-radius relationship of a static, spherical symmetric neutron star. Results are compared to published values of the properties of saturated nuclear matter and to available observational data of the mass-radius relationship of neutron stars.