Permutation Phase and Gentile Statistics
- URL: http://arxiv.org/abs/2001.02830v1
- Date: Thu, 9 Jan 2020 04:16:13 GMT
- Title: Permutation Phase and Gentile Statistics
- Authors: Qiang Zhang, Bin Yan
- Abstract summary: It is shown that a finite textitcapacity q -- the maximally allowed particle occupation of each quantum state, naturally arises.
The relation between the permutation phase and capacity is given, interpolating between fermions and bosons in the sense of both exchange phase and occupation number.
- Score: 13.505175620668993
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: This paper presents a new way to construct single-valued many-body
wavefunctions of identical particles with intermediate exchange phases between
Fermi and Bose statistics. It is demonstrated that the exchange phase is not a
representation character but the \textit{word metric} of the permutation group,
beyond the anyon phase from the braiding group in two dimensions. By
constructing this type of wavefunction from the direct product of
single-particle states, it is shown that a finite \textit{capacity q} -- the
maximally allowed particle occupation of each quantum state, naturally arises.
The relation between the permutation phase and capacity is given, interpolating
between fermions and bosons in the sense of both exchange phase and occupation
number. This offers a quantum mechanics foundation for \textit{Gentile
statistics} and new directions to explore intermediate statistics and anyons.
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