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Transfer matrices for the totally asymmetric exclusion process (1001.1064v1)
Published 7 Jan 2010 in cond-mat.stat-mech
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.
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