Matrix product solution of the multispecies partially asymmetric exclusion process

Details Matrix product solution of the multispecies partially asymmetric exclusion process Matrix product solution of the multispecies partially asymmetric exclusion process

2008-12-17

arxiv.org/abs/0812.3293v3

J. Phys. A: Math. Theor. 42 (2009) 165004

Physics

Condensed Matter

Statistical Mechanics

27 pages, 3 figures

Scientific paper

10.1088/1751-8113/42/16/165004

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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