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Physica A Statistical Mechanics and its Applications

The relation between properties of Gentile statistics and fractional statistics of anyon

Yao Shen, Qing Ai, Gui Lu Long

Published Jan 5, 2010• 20 citations
Publisher
DOI
10.1016/j.physa.2009.12.042

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Abstract Gentile statistics describes fractional statistical systems in the occupation number representation. Anyon statistics researches those systems in the winding number representation. Both of them are intermediate statistics between Bose–Einstein and Fermi–Dirac statistics. The second quantization of Gentile statistics shows a lot of advantages. According to the symmetry requirement of the wave function and the property of braiding, we give the general construction of transformation between anyon and Gentile statistics. In other words, we introduce the second quantization form of anyons in an easier way. This construction is a correspondence between two fractional statistics and gives a new description of anyon. Basic relations of second quantization operators, the coherent state and Berry phase are also discussed.
The many-anyons wavefunction is constructed via the superposition of all the permutations on the direct product of single anyon states and its interchange properties are examined. The phase of permutation is not a representation but the word metric of the permutation group . Amazingly the interchange phase yields a finite capacity of one quantum state interpolating between Fermion and Boson and the mutual exchange phase has no explicit effect on statistics. Finite capacity of quantum state is defined as Gentile statistics and it is different from the fractional exclusion statistics. Some discussion on the general model is also given.