Mi Xie

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

An approach for the calculation of one-loop effective actions, vacuum energies, and spectral counting functions

. 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

Intermediate-statistics spin waves

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

The pressure exerted by a confined ideal gas

and

An intermediate distribution between Gaussian and Cauchy distributions

n=1

An exactly solvable phase transition model: generalized statistics and generalized Bose-Einstein condensation

. The energy spectrum of such an intermediate-statistics oscillator is calculated. Finally, we discuss the intermediate-statistics representation of angular momentum [su(2)] algebra. Moreover, a further study of the operator realization of intermediate statistics is given in the Appendix.