Inhomogeneous discrete-time exclusion processes

Nicolas Crampé (1) , K. Mallick (2) , E. Ragoucy (3) , M. Vanicat (3)

1 L2C - Laboratoire Charles Coulomb
2 IPHT - Institut de Physique Théorique - UMR CNRS 3681
3 LAPTH - Laboratoire d'Annecy-le-Vieux de Physique Théorique

We study discrete time Markov processes with periodic or open boundaryconditions and with inhomogeneous rates in the bulk. The Markov matrices aregiven by the inhomogeneous transfer matrices introduced previously to prove theintegrability of quantum spin chains. We show that these processes have asimple graphical interpretation and correspond to a sequential update. Wecompute their stationary state using a matrix ansatz and express theirnormalization factors as Schur polynomials. A connection between Bethe rootsand Lee-Yang zeros is also pointed out.

Domaines: Mécanique statistique [cond-mat.stat-mech]

Nicolas Crampé, K. Mallick, E. Ragoucy, M. Vanicat. Inhomogeneous discrete-time exclusion processes. Journal of Physics A: Mathematical and Theoretical, 2015, 48 (48), pp.484002. ⟨10.1088/1751-8113/48/48/484002⟩. ⟨hal-01180460⟩