Two-species hardcore reversible cellular automaton: matrix ansatz for dynamics and nonequilibrium stationary state
Marko Medenjak, Vladislav Popkov, Tomaž Prosen, Eric Ragoucy, Matthieu Vanicat
SciPost Phys. 6, 074 (2019) · published 24 June 2019
In this paper we study the statistical properties of a reversible cellular automaton in two out-of-equilibrium settings. In the first part we consider two instances of the initial value problem, corresponding to the inhomogeneous quench and the local quench. Our main result is an exact matrix product expression of the time evolution of the probability distribution, which we use to determine the time evolution of the density profiles analytically. In the second part we study the model on a finite lattice coupled with stochastic boundaries. Once again we derive an exact matrix product expression of the stationary distribution, as well as the particle current and density profiles in the stationary state. The exact expressions reveal the existence of different phases with either ballistic or diffusive transport depending on the boundary parameters.
Cited by 1
Katja Klobas et al., Time-Dependent Matrix Product Ansatz for Interacting Reversible Dynamics
Commun. Math. Phys. 371, 651 (2019) [Crossref]
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- 1 École Normale Supérieure [ENS]
- 2 Bergische Universität Wuppertal / University of Wuppertal [BUW]
- 3 Universität zu Köln / University of Cologne [UoC]
- 4 Univerza v Ljubljani / University of Ljubljana [UL]
- 5 Universite Grenoblé Alpes / Grenoble Alpes University [UGA]
- 6 Laboratoire d'Annecy-le-Vieux de Physique Théorique [LAPTh]