Random Point Field Approach to Analysis of Anisotropic Bose - Einstein Condensations
2012, v.18, Issue 3, 473-530
Position distributions of constituent particles of the perfect Bose-gas trapped in exponentially and polynomially anisotropic boxes are investigated by means of the boson random point fields (processes) and by the spatial random distribution of particle density. Our results include the case of generalised Bose - Einstein Condensation. For exponentially anisotropic quasi two-dimensional system (SLAB), we obtain three qualitatively different particle density distributions. They correspond to the normal phase, the quasi-condensate phase (type III generalised condensation) and to the phase when the type III and the type I Bose condensations coexist. An interesting feature is manifested by the type II generalised condensation in one-directional polynomially anisotropic system (BEAM). In this case the particle density distribution rests truly random (undecomposable into "deterministic" fields) even in the macroscopic scaling limit.
Keywords: random point fields (processes),quantum statistical mechanics,Bose - Einstein condensation,anisotropic systems,spatial particle density