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.

General Quantum Theory No Axiom Presumption: II ----Measuring and Identical Theorems, Origins & Classifications of Entanglements and Solution to Crisis of Wave Collapse

“…Collapse effect in classical statistical mechanics [2,3]: A density state means that a particle is in a density state of multiple superposition possibilities, but once an observer has observed it, it can only fall into a density state of specific possibility. Although each measurement must collapse to some possible density state, a large number of observations reveal a probability density distribution, which just shows that the matter is described by probability density.…”

“…(2.6), respectively, show the classical locality and quantum non-locality for any n particle system, 7) directly, respectively, shows the classical locality and quantum non-locality for any n particle system. According to classical statistical mechanics [2,3], when a system is not measured, it evolves according to its own classical statistical mechanics. When measured in the sample space of classical statistical mechanics, any physical quantity measurements are collapsing at a certain probability to observe the state, because we have already taken the micro-particle system state described by a general complex function of square root of density function (It can be called the square root of the probability density function, which is projected onto the plane wave and doing their Fourier integration), so we have entered a special system different from the classical statistical mechanics description of the system, we call it a quantum mechanics system.…”

“…These measurement processes are nonlocal, decoherent, stochastic and irreversible even from the classical statistical point of view, because classical measures cause the taking eigenvalue corresponding to the variational system's choosing extreme value in process transforming classical statistical mechanics to quantum mechanics and in the quantum mechanics so that people can measure the eigenvalues. On the bases of the nonlocal, decoherent, randomness and irreversibility of these classical statistical mechanics ( which have been understood no problem in classical statistical mechanics [3]) , the nonlocal, decoherent, randomness and irreversibility of plane waves of any n particles are superimposed. Therefore, these properties of nonlocal, decoherent, random and irreversible measurement collapse caused by quantum mechanics measurement collapse are thoroughly proved and understood in the systems.…”

“…In classical statistical mechanics, when the identical particles of a system have indiscernible property, the physical state of the system composed of identical particles will not be changed due to the exchange of identical particles, and the particles with all intrinsic properties such as the same mass, charge, spin and isospin can be called identical particles [2,3].…”

“…Statistical mechanics can be used to explain the thermodynamic behaviors of large systems, and shows how the concepts from macroscopic observations, e.g., temperature & pressure, are relevant to microscopic states of fluctuating around an average state. It links thermodynamic quantities, e.g., heat capacity, to microscopic behaviors [3].…”