Multiple Exclusion Statistics

Abstract

A new distribution for systems of particles in equilibrium obeying exclusion of correlated states is presented following the Haldane's state counting. It relies upon an ansatz to deal with the multiple exclusion that takes place when the states accessible to single particles are spatially correlated and it can be simultaneously excluded by more than one particle. The Haldane's statistics and Wu's distribution are recovered in the limit of non-correlated states of the multiple exclusion statistics. In addition, an exclusion spectrum function $\mathcal{G}(n)$ is introduced to account for the dependence of the state exclusion on the occupation-number $n$. Results of thermodynamics and state occupation are shown for ideal lattice gases of linear particles of size $k$ ($k$-mers) where multiple exclusion occurs. Remarkable agreement is found with Grand-Canonical Monte Carlo simulations from $k$=2 to 10 where multiple exclusion dominates as $k$ increases.

5 pages, 3 figures. Final version to be published in Physical Review Letters

References in corpus (7)

• Realization of a Laughlin quasiparticle interferometer: Observation of fractional statistics
• Sub-Poissonian fluctuations in a 1D Bose gas: from the quantum quasi-condensate to the strongly interacting regime
• The 1D interacting anyon gas: low-energy properties and Haldane exclusion statistics
• On the orientational ordering of long rods on a lattice
• The nematic-disordered phase transition in systems of long rigid rods on two dimensional lattices
• Phase transitions in a system of hard rectangles on the square lattice
• Multiple Exclusion Statistics: the $k$-mers problem

Cited by in corpus (2)

• Hyperuniformity and conservation laws in non-equilibrium systems
• Derivation of a statistical model for classical systems obeying fractional exclusion principle