Physicists become acquainted with special functions early in their studies. Consider our
perennial model, the harmonic oscillator, for which we need Hermite functions, or the …

We review the phenomenon of equilibrium fluctuations in the number of condensed atoms n
0 in a trap containing N atoms total. We start with a history of the Bose–Einstein distribution …

We find the universal structure and scaling of the Bose-Einstein condensation (BEC)
statistics and thermodynamics (Gibbs free energy, average energy, heat capacity) for a …

We analytically calculate the critical phenomena of a Bose-Einstein condensation of an ideal
gas in an arbitrary trap with any mesoscopic or macroscopic number of particles and find all …

We consider the path-integral representation of the ideal Bose gas under various boundary
conditions. We show that Bose--Einstein condensation occurs at the famous critical density …

Using a field-theoretic approach, we systematically generalize the usual semiclassical
approximation for a harmonically trapped ideal Bose gas in such a way that its range of …

We find a self-similar analytical solution for the grand-canonical-ensemble (GCE) statistics
and thermodynamics in the critical region of Bose–Einstein condensation. It is valid for an …

The problem to express a natural number N as a product of natural numbers without regard
to order corresponds to a thermally isolated non-interacting Bose gas in a one-dimensional …

We conduct a rigorous investigation into the thermodynamic instability of an ideal Bose gas
confined in a cubic box, without assuming a thermodynamic limit or a continuous …

The number partitioning problem can be interpreted physically in terms of a thermally
isolated noninteracting Bose gas trapped in a one-dimensional harmonic-oscillator …