Relations between intermediate statistics and quantum statistics

摘要

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.