Related papers: Some typical delusions in the theory of Bose-Einst…
Major issues arising in the theory of Bose-Einstein condensation are reviewed. These issues, although being principally important, are very often misunderstood, which results in wrong conclusions. The basic point is global gauge symmetry…
The fundamental problem is analized, the relation between Bose-Einstein condensation and spontaneous gauge symmetry breaking. This relation is largerly misunderstood in physics community. Numerous articles and books contain the statement…
The realisation of Bose-Einstein condensation under grand-canonical conditions has provided the experimental evidence for the simultaneous occurrence of macroscopic fluctuations and phase coherence of the condensate. The observation of…
The interplay between spontaneously broken gauge symmetries and Bose-Einstein condensation has long been controversially discussed in science, since the equation of motions are invariant under phase transformations. Within the present model…
The review is devoted to the elucidation of the basic problems arising in the theoretical investigation of systems with Bose-Einstein condensate. Understanding these challenging problems is necessary for the correct description of…
We examine Bose-Einstein condensation as a form of symmetry breaking in the specific model of the Einstein static universe. We show that symmetry breaking never occursin the sense that the chemical potential $\mu$ never reaches its critical…
Adding a gauge symmetry breaking field -\nu\sqrt{V}(a_0+a_0^*) to the Hamiltonian of some simplified models of an interacting Bose gas we compute the condensate density and the symmetry breaking order parameter in the limit of infinite…
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…
We consider the self-evolution of strongly non-equilibrium interacting Bose gas. Due to the mere fact of large (as compared to unity) occupation numbers in the initial state the problem is directly reduced to the question of temporal…
The behavior of an ideal $D$-dimensional boson gas in the presence of a uniform gravitational field is analyzed. It is explicitly shown that, contrarily to an old standing folklore, the three-dimensional gas does not undergo Bose-Einstein…
These notes present simple theoretical approaches to study Bose-Einstein condensation in trapped atomic gases and their comparison to recent experimental results : - the ideal Bose gas model - Fermi pseudopotential to model the atomic…
Evading the Mermin-Wagner-Hohenberg no-go theorem and revisiting with rigor the ideal Bose gas confined in a square box, we explore a discrete phase transition in two spatial dimensions. Through both analytic and numerical methods we verify…
A gaseous Bose-Einstein condensate (BEC) offers an ideal testing ground for studying symmetry breaking, because a trapped BEC system is in a mesoscopic regime, and situations exist under which symmetry breaking may or may not occur.…
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…
The paradox of Bose-Einstein condensation is that phenomena such as the $\lambda$-transition heat capacity and superfluid flow are macroscopic, whereas the occupancy of the ground state is microscopic. This contradiction is resolved with a…
Bose-condensed gases are considered with an effective interaction strength varying in the whole range of the values between zero and infinity. The consideration is based on the usage of a representative statistical ensemble for Bose systems…
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:…
The stability of a Bose condensed gas with a negative scattering length is studied with regard to the role played by the initial state. A trapped ideal gas ground state is shown to be unstable when the Gross Pitaevskii equation still…
Bose-Einstein condensation represents a remarkable phase transition, characterized by the formation of a single quantum subsystem. As a result, the statistical properties of the condensate are highly unique. In the case of a Bose gas, while…
The notion of fluctuation indices, characterizing thermodynamic stability of statistical systems, is advanced. These indices are especially useful for investigating the stability of nonuniform and trapped atomic assemblies. The fluctuation…