Statistical mechanics and the physics of many-particle model systems

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.Keywords: Quantum statistical physics; quantum theory of magnetism; theory of superconductivity; Green's function method; Hubbard model and other many-particle models on a lattice; symmetry principles; breaking of symmetries; Bogoliubov's quasiaverages; quasiparticle many-body dynamics; magnetic polaron; microscopic theory of the antiferromagnetism.

Dynamics of a Bose-Einstein condensate of excited magnons

“…As noticed in the Introduction we resort to the use of NESEF. According to the formalism, following Mori, Zwanzig and others [31,32,33,34,35,36], the Hamiltonian of the system under consideration is separated out in a so-called relevant partĤ 0 , consisting of the energy operators of the free degrees of freedom, andĤ ′ containing the interactions among them and the coupling with external sources and reservoirs. In our case herê…”

“…The formalism introduces the fundamental properties of historicity and irreversibility in the evolution of the nonequilibrium system where dissipative and pumping processes are under way. In terms of the dynamics generated by this full Hamiltonian the equations of evolution of the macroscopic state of the system are obtained in the framework of the NESEF-based nonlinear quantum kinetic theory [31,32,33,34,35,36,40,41,42,43]. We call the attention to the fact that the evolution equations are the quantum mechanical equations of motion averaged over the nonequilibrium ensemble, with the NESEF-kinetic theory providing a practical way of calculation.…”

“…The microscopic state of the system is characterized by the full Hamiltonian of spins and lattice vibrations after going through Holstein-Primakov and Bogoliubov transformations [28,29,30]. On the other hand, the characterization of the macroscopic state of the magnon system is done in terms of the Thermo-Mechanical Statistics based on the framework of a Non-Equilibrium Statistical Ensemble Formalism (NESEF for short) [31,32,33,34,35,36]. Other modern approach consists in the use of Computational Modeling [37,38] (developed after Non-equilibrium Molecular Dynamics [39]).…”

Quasiaverages, symmetry breaking and irreducible Green functions method

“…However, this was a phenomenological approach that did not reveal the nature of relevant interactions. An alternative way of viewing quasiparticles, more general and consistent, is through the Green function scheme of many-body theory [19,22,28,29]. It becomes clear that only a thorough experimental and theoretical investigation of quasiparticle many-body dynamics of the many-particle systems can provide an answer to the relevant microscopic picture [22].…”

Ultrafast Transport Transient in n-Doped ZnS in Wurtzite and Zincblende Phases

“…For this, we used a kinetic theory for far-from equilibrium systems: the "Non-Equilibrium Statistical Operator Method" [15], which provides an elegant, practical, and physically clear picture of irreversible processes [16,17]; for example, in far-from equilibrium semiconductors [18][19][20][21][22], which is the case considered here. This method was used in numerous works for studying transport processes and kinetic phenomena (e.g., [23][24][25]). …”