Generalized matrix Ansatz in the multispecies exclusion process - partially asymmetric case

Abstract

We investigate one of the simplest multispecies generalization of the asymmetric simple exclusion process on a ring. This process has a rich combinatorial spectral structure and a matrix product form for the stationary state. In the totally asymmetric case operators that conjugate the dynamics of systems with different numbers of species were obtained by the authors and reported recently. The existence of such nontrivial operators was reformulated as a representation problem for a specific quadratic algebra (generalized matrix Ansatz). In the present work, we construct the family of representations explicitly for the partially asymmetric case. This solution cannot be obtained by a simple deformation of the totally asymmetric case.

References in corpus (8)

• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• The asymmetric simple exclusion process: an integrable model for non-equilibrium statistical mechanics
• Matrix representation of the stationary measure for the multispecies TASEP
• Microscopic versus macroscopic approaches to non-equilibrium systems
• Some Exact Results for the Exclusion Process
• Spectrum in multi-species asymmetric simple exclusion process on a ring
• Algebraic Bethe Ansatz for the two species ASEP with different hopping rates
• Recursive structures in the multispecies TASEP

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