Two-species hardcore reversible cellular automaton: matrix ansatz for dynamics and nonequilibrium stationary state

Medenjak, Marko; Popkov, Vladislav; Prosen, Tomaž; Ragoucy, Eric; Vanicat, Matthieu

doi:10.21468/SciPostPhys.6.6.074

SciPost Physics

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

doi: 10.21468/SciPostPhys.6.6.074
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Abstract

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.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.6.6.074
TI  - Two-species hardcore reversible cellular automaton: matrix ansatz for dynamics and nonequilibrium stationary state
PY  - 2019/06/24
UR  - https://www.scipost.org/SciPostPhys.6.6.074
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 6
IS  - 6
SP  - 074
A1  - Medenjak, Marko
AU  - Popkov, Vladislav
AU  - Prosen, Tomaž
AU  - Ragoucy, Eric
AU  - Vanicat, Matthieu
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.6.6.074,
	title={{Two-species hardcore reversible cellular automaton: matrix ansatz for dynamics and nonequilibrium stationary state}},
	author={Marko Medenjak and Vladislav Popkov and Tomaž Prosen and Eric Ragoucy and Matthieu Vanicat},
	journal={SciPost Phys.},
	volume={6},
	pages={074},
	year={2019},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.6.6.074},
	url={https://scipost.org/10.21468/SciPostPhys.6.6.074},
}

Cited by 12

Ontology / Topics

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Bethe Ansatz Cellular automata Out-of-equilibrium systems Stochastic dynamics

Authors / Affiliations: mappings to Contributors and Organizations

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¹ Marko Medenjak,
² ³ ⁴ Vladislav Popkov,
⁴ Tomaž Prosen,
⁵ ⁶ Eric Ragoucy,
⁴ Matthieu Vanicat

Funders for the research work leading to this publication