Study of a Non-Interacting Boson Gas

Abstract

For a non-interacting many particle Bose system whose energy operator is diagonal in the number of occupation operatorsn j upper bounds on the thermal averages n j are obtained. These bounds lead to the proof of Bose-Einstein condensation for finite values of the inverse temperature β and for chemical potential µ = 0. Finally for µ < 0, in the case of a generalization of the studied model system, the property of Local Gaussian Domination for the grand canonical partition function is proved.

Fundamental Principles of Theoretical Physics and Concepts of Quasiaverages, Quantum Protectorate and Emergence

“…In this framework the 1/q 2 -type properties in the theory of the superfluidity of Bose and Fermi systems, the properties of basic Green functions for a Bose system in the presence of condensate, and a model with separated condensate were analyzed [52] . The method of quasiaverages is a constructive workable scheme for studying systems with spontaneous symmetry breakdown such as superluidity and superconductivity [15,16,33,52,53,54,55,56,57,58,59,60,61,62]. A quasiaverage is a thermodynamic (in statistical mechanics) or vacuum (in quantum field theory) average of dynamical quantities in a specially modified averaging procedure, enabling one to take into account the effects of the influence of state degeneracy of the system.…”