The equilibrium states of the free Boson gas

Abstract

The generating functional of the cyclic representation of the canonical commutation relations for the equilibrium state of the free Boson gas is calculated, using a method due to Kac, as the thermodynamic limit of the grand canonical generating functional. The relation to the work of Araki and Woods is discussed.

Bose-Einstein condensation of scalar fields on hyperbolic manifolds

“…From this point on, the mathematical analysis of the infinite volume limit exactly parallels the one in flat space for non relativistic systems, as it is done in various references [25,26,4]. In particular, there is a critical temperature T c over which there are no particles in the ground state.…”

Large deviation principle for noninteracting boson random point processes

“…The specificity of the BEC is that it is a quantum phase transition with particular properties of the quantum fluctuations. 11,20 Finally, we would like to mention a special case of the critical point: = c . In this case the boson RPF is defined by the measure c = K z=1 ␤ ͑det͒ and it corresponds to the so-called critical fluctuations, which should be considered separately.…”

Mean-field interacting boson random point fields in weak harmonic traps

“…3 and 14. Similarly, it is well known that thermodynamic properties of the boson gases are very sensible to different ways of taking the thermodynamic limit 9 or to the different choices of the boundary conditions. 21 The purpose of this paper is to examine the position distribution of the mean-field boson model in WHT limit and to compare its behavior to those of the mean-field boson models in TDL or ideal boson models in WHT limit.…”