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arXiv:hep-th/9411236

Exclusion statistics and many-particle states

P. Mitra

Published Nov 30, 1994• 2 citations
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Abstract

The thermodynamic distribution function for exclusion statistics is derived. Creation and annihilation operators for particles obeying such statistics are discussed. A connection with anyons is pointed out.
DOI
10.48550/arxiv.hep-th/9411236

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We derive some physical properties of ideal assemblies of identical particles obeying generalized exclusion statistics. We discuss fluctuations and in this connection point out a fundamental contrast to conventional quantum statistics. We demonstrate a duality relating the distribution of particles at statistics ggg to the distribution of holes at statistics 1g\frac{1}{g}g1​. We suggest an application to Mott insulators.
We derive some physical properties of ideal assemblies of identical particles obeying generalized exclusion statistics. We discuss fluctuations, and in this connection point out a fundamental contrast to conventional quantum statistics. We demonstrate a duality relating the distribution of particles at statistics ggg to the distribution of holes at statistics 1/g1/g1/g. We suggest applications to Mott insulators.
A new distribution for systems of particles obeying statistical exclusion of correlated states is presented following the Haldane's state counting. It relies upon a conjecture to deal with the multiple exclusion that takes place when the states available to single particles are spatially correlated and it can be simultaneously excluded by more than one particle. The Haldane's statistics [F. D. M. Haldane, Phys. Rev. Lett. 67, 937 (1991)] and Wu's distribution [Y.-S. Wu, Phys. Rev. Lett. 52, 2103 (1984)] are recovered in the limit of non-correlated states (constant statistical exclusion) of the multiple exclusion statistics. In addition, the exclusion spectrum function G(n)G(n)G(n) is introduced to account for the dependence of the statistical exclusion on the occupation-number nnn. Results of thermodynamics and state occupation are shown for ideal lattice gases of linear particles of size kkk (kkk-mers) where multiple exclusion occurs. Remarkable agreement is found with simulations from k=2k=2k=2 to 101010 where multiple exclusion dominates as kkk increases.
I discuss Haldane's concept of generalized exclusion statistics (1991 Phys. Rev. Lett. 67 937) and show that it leads to inconsistencies in the calculation of the particle distribution that maximizes the partition function. These inconsistencies appear when mutual exclusion statistics is manifested between different subspecies of particles in the system. In order to eliminate these inconsistencies, I introduce new mutual exclusion statistics parameters, which are proportional to the dimension of the Hilbert subspace on which they act. These new definitions lead to properly defined particle distributions and thermodynamic properties. In another paper ( Preprint 0710.0728), I show that the fractional exclusion statistics manifested in general systems with interaction have these, physically consistent, statistics parameters.
We show that below the degenerate temperature the distribution profiles of strongly interacting anyons in one-dimension coincide with the most probable distributions of ideal particles obeying generalized exclusion statistics (GES). In the strongly interacting regime the thermodynamics and the local two-particle correlation function derived from the GES are seen to agree for low temperatures with the results derived for the anyon model using the thermodynamic Bethe ansatz. The anyonic and dynamical interactions implement a continuous range of GES, providing a signature of strongly interacting anyons, including the strongly interacting one-dimensional Bose gas.