Statistical Mechanics and the Physics of the ManyParticle Model Systems
Abstract
The development of methods of quantum statistical mechanics is considered in light of their applications to quantum solidstate theory. We discuss fundamental problems of the physics of magnetic materials and the methods of the quantum theory of magnetism, including the method of twotime temperature Green's functions, which is widely used in various physical problems of manyparticle 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 spinfermion model are considered in the framework of novel selfconsistentfield 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.
 Publication:

arXiv eprints
 Pub Date:
 January 2011
 arXiv:
 arXiv:1101.3423
 Bibcode:
 2011arXiv1101.3423K
 Keywords:

 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 77 pages, 1 figure, Refs.376