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

Abstract

In this paper, we first discuss the general properties of an intermediate-statistics quantum bracket, ${[u,v]}_{n}=uv\ensuremath{-}{e}^{i2\ensuremath{\pi}∕(n+1)}vu$, which corresponds to intermediate statistics in which the maximum occupation number of one quantum state is an arbitrary integer, $n$. 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 $n\ensuremath{\rightarrow}\ensuremath{\infty}$ and $n=1$. 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.