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.

27 pages, 3 figures

References in corpus (3)

• Exact Spectral Gaps of the Asymmetric Exclusion Process with Open Boundaries
• Current Fluctuations in the exclusion process and Bethe Ansatz
• Fluctuations and skewness of the current in the partially asymmetric exclusion process

Cited by in corpus (1)

• Spectrum in multi-species asymmetric simple exclusion process on a ring