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

Medenjak, Marko (author), Popkov, Vladislav (author), Prosen, Tomaž (author), Ragoucy, Eric (author), Vanicat, Matthieu (author)

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.

• Language: English
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2019
• Number of pages: 37 str.
• Numbering: Vol. 6, art. no. 074
• PID: 20.500.12556/RUL-111524
• UDC: 536.9
• ISSN on article: 2542-4653
• DOI: 10.21468/SciPostPhys.6.6.074
• COBISS.SI-ID: 3367268
• Publication date in RUL: 02.10.2019

Record is a part of a journal

• Title: SciPost physics
• Publisher: SciPost Foundation
• ISSN: 2542-4653
• COBISS.SI-ID: 526154521

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.
• Licensing start date: 02.10.2019

Projects

• Funder: EC - European Commission
• Funding programme: H2020
• Project number: 694544
• Name: Open many-body non-equilibrium systems
• Acronym: OMNES