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Matrix product solution of the multispecies partially asymmetric exclusion process

Abstract : We find the exact solution for the stationary state measure of the partially asymmetric exclusion process on a ring with multiple species of particles. The solution is in the form of a matrix product representation where the matrices for a system of N species are defined recursively in terms of the matrices for a system of N-1 species. A complete proof is given, based on the quadratic relations verified by these matrices. This matrix product construction is interpreted in terms of the action of a transfer matrix.
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https://hal.archives-ouvertes.fr/hal-00796157
Contributor : Sylvain Prolhac <>
Submitted on : Friday, March 1, 2013 - 5:10:02 PM
Last modification on : Wednesday, April 14, 2021 - 12:12:24 PM

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Sylvain Prolhac, Martin R. Evans, Kirone Mallick. Matrix product solution of the multispecies partially asymmetric exclusion process. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2009, 42 (16), pp.165004. ⟨10.1088/1751-8113/42/16/165004⟩. ⟨hal-00796157⟩

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