Transfer matrices for the totally asymmetric exclusion process

Abstract

We consider the totally asymmetric simple exclusion process (TASEP) on a finite lattice with open boundaries. We show, using the recursive structure of the Markov matrix that encodes the dynamics, that there exist two transfer matrices $T_{L-1,L}$ and ${\tilde{T}}_{L-1,L}$ that intertwine the Markov matrices of consecutive system sizes: ${\tilde{T}}_{L-1,L}{M}_{L-1}=M_L{T}_{L-1,L}$. This semi-conjugation property of the dynamics provides an algebraic counterpart for the matrix-product representation of the steady state of the process.

7 pages

References in corpus (5)

• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• Matrix representation of the stationary measure for the multispecies TASEP
• Matrix product solution of the multispecies partially asymmetric exclusion process
• Spectrum in multi-species asymmetric simple exclusion process on a ring
• Exact results for an asymmetric annihilation process with open boundaries

Cited by in corpus (3)

• Some Exact Results for the Exclusion Process
• Recursive structures in the multispecies TASEP
• Lattice SUSY for the DiSSEP at ${\lambda }^2=1$ (and ${\lambda }^2=-3$)