Geometry effects in confined space

In this paper we calculate some exact solutions of the grand partition functions for quantum gases in confined space, such as ideal gases in two- and three-dimensional boxes, in tubes, in annular containers, on the lateral surface of cylinders, and photon gases in three-dimensional boxes. Based on these exact solutions, which, of course, contain the complete information about the system, we discuss the geometry effect which is neglected in the calculation with the thermodynamic limit $V\to \infty$, and analyze the validity of the quantum statistical method which can be used to calculate the geometry effect on ideal quantum gases confined in two-dimensional irregular containers. We also calculate the grand partition function for phonon gases in confined space. Finally, we discuss the geometry effects in realistic systems.Comment: Revtex,15 pages, no figur

Do bosons obey Bose-Einstein distribution: two iterated limits of Gentile distribution

It is a common impression that by only setting the maximum occupation number to infinity, which is the demand of the indistinguishability of bosons, one can achieve the statistical distribution that bosons obey -- the Bose-Einstein distribution. In this letter, however, we show that only with an infinite maximum occupation number one cannot uniquely achieve the Bose-Einstein distribution, since in the derivation of the Bose-Einstein distribution, the problem of iterated limit is encountered. For achieving the Bose-Einstein distribution, one needs to take both the maximum occupation number and the total number of particles to infinities, and, then, the problem of the order of taking limits arises. Different orders of the limit operations will lead to different statistical distributions. For achieving the Bose-Einstein distribution, besides setting the maximum occupation number, we also need to state the order of the limit operations.Comment: 6 pages, no figur

Quantum statistics of ideal gases in confined space

In this paper, the effects of boundary and connectivity on ideal gases in two-dimensional confined space and three-dimensional tubes are discussed in detail based on the analytical result. The implication of such effects on the mesoscopic system is also revealed.Comment: 7 pages, Late

The explicit expression of the fugacity for weakly interacting Bose and Fermi gases

In this paper, we calculate the explicit expression for the fugacity for two- and three-dimensional weakly interacting Bose and Fermi gases from their equations of state in isochoric and isobaric processes, respectively, based on the mathematical result of the boundary problem of analytic functions --- the homogeneous Riemann-Hilbert problem. We also discuss the Bose-Einstein condensation phase transition of three-dimensional hard-sphere Bose gases.Comment: 24 pages, 9 figure