Statistical Mechanics and the Physics of the Many-Particle Model Systems

TL;DR

This paper reviews quantum statistical mechanics methods applied to many-particle systems, focusing on magnetic materials, quasiparticle dynamics, and models like Heisenberg and Hubbard, highlighting their applications and fundamental concepts.

Contribution

It provides a comprehensive analysis of quantum models of magnetism, comparing their applicability and discussing advanced concepts like broken symmetry and quantum protectorates.

Findings

Comparison of models for magnetic materials

Application of Green's functions in quantum magnetism

Analysis of dissipative effects in particle dynamics

Abstract

The development of methods of quantum statistical mechanics is considered in light of their applications to quantum solid-state theory. We discuss fundamental problems of the physics of magnetic materials and the methods of the quantum theory of magnetism, including the method of two-time temperature Green's functions, which is widely used in various physical problems of many-particle systems with interaction. Quantum cooperative effects and quasiparticle dynamics in the basic microscopic models of quantum theory of magnetism: the Heisenberg model, the Hubbard model, the Anderson Model, and the spin-fermion model are considered in the framework of novel self-consistent-field approximation. We present a comparative analysis of these models; in particular, we compare their applicability for description of complex magnetic materials. The concepts of broken symmetry, quantum protectorate, and quasiaverages are analyzed in the context of quantum theory of magnetism and theory of superconductivity. The notion of broken symmetry is presented within the nonequilibrium statistical operator approach developed by D.N. Zubarev. In the framework of the latter approach we discuss the derivation of kinetic equations for a system in a thermal bath. Finally, the results of investigation of the dynamic behavior of a particle in an environment, taking into account dissipative effects, are presented.