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arXiv · 0705.2382

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

Yao Shen·Wu-Sheng Dai·Mi Xie
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Abstract

In this paper, we first discuss the general properties of an intermediate-statistics quantum bracket, $[ u,v]_{n}=uv-e^{i2π/(n+1)}vu$, 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\to \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.

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Yao Shen, Wu-Sheng Dai, Mi Xie. 2007-05-16. Intermediate-statistics quantum bracket, coherent state, oscillator, and representation of angular momentum (su(2)) algebra. https://doi.org/10.1103/physreva.75.042111

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