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.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.

arXiv:0705.2382Physical Review AApr 23, 200730 citations

Quantum Statistics

Marius Grundmann

Graduate texts in physicsJan 1, 20100 citations

The no-Cloning Theorem Based on a Statistical Model

Koji Nagata, Tadao Nakamura

We investigate the no-cloning theorem that relies on the properties of a statistical model. Usually, the no-cloning theorem implies that two quantum states are identical or orthogonal if we allow a cloning to be on the two quantum states. Here, we rely on a statistical model. We may result in the fact that the two quantum states under consideration could not be orthogonal if we accept the statistical model. The no-cloning theorem may imply that the two quantum states under consideration may be identical if we accept the statistical model. The no-cloning theorem itself has this character.We investigate the no-cloning theorem that relies on the properties of a statistical model. Usually, the no-cloning theorem implies that two quantum states are identical or orthogonal if we allow a cloning to be on the two quantum states. Here, we rely on a statistical model. We may result in the fact that the two quantum states under consideration could not be orthogonal if we accept the statistical model. The no-cloning theorem may imply that the two quantum states under consideration may be identical if we accept the statistical model. The no-cloning theorem itself has this character.

Sep 1, 20180 citations

RELATIONS BETWEEN INTERMEDIATE STATISTICS AND QUANTUM STATISTICS

Pengfei Ma, Chi-Chun Zhou, Yu-Zhu Chen +1 more

We provide the relations among intermediate, Bose and Fermi statistics through a simplified quantum dot model. We show that the high-temperature (near-classical) behavior of the intermediate statistics is like the Bose statistics: We develop the virial expansion of the intermediate statistics, and find that the first n (maximum occupation number on a single state) expansion coefficients are the same as the corresponding Bose virial coefficients. We also show that under low-temperature (near-quantum) conditions, the n-intermediate statistics on a single state behaves more like the Fermi statistics on an n-degenerate state.We provide the relations among intermediate, Bose and Fermi statistics through a simplified quantum dot model. We show that the high-temperature (near-classical) behavior of the intermediate statistics is like the Bose statistics: We develop the virial expansion of the intermediate statistics, and find that the first n (maximum occupation number on a single state) expansion coefficients are the same as the corresponding Bose virial coefficients. We also show that under low-temperature (near-quantum) conditions, the n-intermediate statistics on a single state behaves more like the Fermi statistics on an n-degenerate state.

Modern Physics Letters BNov 15, 20121 citation

Quantum Statistics

Crispin W. Gardiner

Springer series in synergeticsJan 1, 19911 citation

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.