Wu-Sheng Dai

Gentile statistics with a large maximum occupation number

Abstract In Gentile statistics the maximum occupation number can take on unrestricted integers: 1 1 the Bose–Einstein case is not recovered from Gentile statistics as n goes to N. Attention is also concentrated on the contribution of the ground state which was ignored in related literature. The thermodynamic behavior of a ν-dimensional Gentile ideal gas of particle of dispersion E=ps/2m, where ν and s are arbitrary, is analyzed in detail. Moreover, we provide an alternative derivation of the partition function for Gentile statistics.

Quantum statistics of ideal gases in confined space

Abstract In this Letter, 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.

The difference of boundary effects between Bose and Fermi systems

In this paper, we show that there exists an essential difference of boundary effects between Bose and Fermi systems both for Dirichlet and Neumann boundary conditions: at low temperatures and high densities the influence of the boundary on the Bose system depends on the temperature but is independent of the density, but for the Fermi case the influence of the boundary is independent of the temperature but depends on the density, after omitting the negligible high-order corrections. We also show that at high temperatures and low densities the difference of the influence of the boundary between Bose and Fermi systems appears in the next-to-leading order boundary contribution, and the leading boundary contribution is independent of the density. Moreover, for calculating the boundary effects at high temperatures and low densities, since the existence of the boundary modification causes the standard virial expansion to be invalid, we introduce a modified virial expansion.

Intermediate-statistics quantum bracket, coherent state, oscillator, and representation of angular momentum [su(2)] algebra

In this paper, we first discuss the general properties of an intermediate-statistics quantum bracket,

Interacting quantum gases in confined space: Two- and three-dimensional equations of state

{[u,v]}_{n}=uv\ensuremath{-}{e}^{i2\ensuremath{\pi}∕(n+1)}vu

The number of eigenstates: counting function and heat kernel

, which corresponds to intermediate statistics in which the maximum occupation number of one quantum state is an arbitrary integer,

Calculating statistical distributions from operator relations: The statistical distributions of various intermediate statistics

n

A representation of angular momentum (SU(2)) algebra

. A further study of the operator realization of intermediate statistics is given. We construct the intermediate-statistics coherent state. An intermediate-statistics oscillator is constructed, which returns to bosonic and fermionic oscillators respectively when

Scattering theory without large-distance asymptotics

n\ensuremath{\rightarrow}\ensuremath{\infty}

Heat-kernel approach for scattering

and