Related papers: Representative statistical ensembles for Bose syst…
Particle fluctuations in systems, exhibiting Bose-Einstein condensation, are reviewed in order to clarify the basic points that attract high interest and often confront misunderstanding. It is explained that the so-called ``grand canonical…
The structure factor for a Bose system with Bose-Einstein condensate is considered in the frame of the self-consistent mean-field approximation. The accomplished analysis demonstrates the principal importance of the following three points:…
In two-dimensional noncommutive space for the case of both position - position and momentum - momentum noncommuting, a constraint between noncommutative parameters is investigated. The related topic of guaranteeing Bose - Einstein…
The virtues of resolvent algebras, compared to other approaches for the treatment of canonical quantum systems, are exemplified by infinite systems of non-relativistic bosons. Within this framework, equilibrium states of trapped and…
The theory of non-interacting Bose gases is supplemented by a numerical quantum field description with a two-dimensional non-local order parameter that allows the modeling of wave-like atomic correlations and interference effects in the…
This paper considers the issue of Bose-Einstein condensation in a weakly interacting Bose gas with a fixed total number of particles. We use an old current algebra formulation of non-relativistic many body systems due to Dashen and Sharp to…
Within the theory of statistical ensemble, the so-called $\mu PT$ ensemble describes equilibrium systems that exchange energy, particles, and volume with the surrounding. General, model-independent features of volume and particle number…
The role of repulsive interactions in statistical systems of Bose particles is investigated. Three different phenomenological frameworks are considered: a mean field model, an excluded volume model, and a model with a medium dependent…
An asymptotic expansions for the grand partition function of ideal Bose gas in the canonical ensemble with arbitrary number of particles is obtained. It is shown that the expressions found are valid in the whole temperature region, the…
Recent results on effects of Bose-Einstein symmetrization in a system of independently produced particles are interpreted in terms of statistical physics. For a large class of distributions, the effective sizes of the system in momentum and…
It is shown, that Bose-Einstein statistical distributions can occur not only in quantum system, but in classical systems as well. The coherent dynamics of the system, or equivalently autocatalytic dynamics in momentum space of the system is…
The properties of systems with Bose-Einstein condensate in external time-independent random potentials are investigated in the frame of a self-consistent stochastic mean-field approximation. General considerations are presented, which are…
We prove rigorously the occurrence of zero-mode Bose-Einstein condensation for a class of continuous homogeneous systems of boson particles with superstable interactions. This is the first example of a translation invariant continuous…
The emergence of macroscopic coherence in a many-body quantum system is a ubiquitous phenomenon across different physical systems and scales. This Chapter reviews key concepts characterizing such systems (correlation functions,…
The role of background in bosonic quantum statistics is discussed in the frame of a new approach in terms of coherent states. Bosons are indeed detected in different physical situations where they exhibit different and apparently…
Analytical expressions for Bose-Einstein condensation of an ideal Bose gas analyzed within the strictures of non-extensive, generalized thermostatistics are here obtained.
An equilibrium statistical system is known to be stable if the fluctuations of global observables are normal, when their dispersions are proportional to the number of particles, or to the system volume. A general theorem is rigorously…
Statistical mechanics is one of the most comprehensive theories in physics. From a boiling pot of water to the complex dynamics of quantum many-body systems it provides a successful connection between the microscopic dynamics of atoms and…
The resonant formation of nonlinear coherent modes in trapped Bose-Einstein condensates is studied. These modes represent nonground-state Bose condensates. The methods of describing the spectrum of the nonlinear modes are discussed. The…
Asymptotic behavior of a class of nonlinear Schr\"odinger equations are studied. Particular cases of 1D weakly focusing and Bose-Einstein condensates are considered. A statistical approach is presented to describe the stationary probability…