Exact solution of the Floquet-PXP cellular automaton

Wilkinson, Joseph W. P. (author), Klobas, Katja (author), Prosen, Tomaž (author), Garrahan, Juan P. (author)

We study the dynamics of a bulk deterministic Floquet model, the Rule 201 synchronous one-dimensional reversible cellular automaton (RCA201). The system corresponds to a deterministic, reversible, and discrete version of the PXP model, whereby a site flips only if both its nearest neighbors are unexcited. We show that the RCA201 (Floquet-PXP) model exhibits ballistic propagation of interacting quasiparticles—or solitons—corresponding to the domain walls between nontrivial threefold vacuum states. Starting from the quasiparticle picture, we find the exact matrix product state form of the nonequilibrium stationary state for a range of boundary conditions, including both periodic and stochastic. We discuss further implications of the integrability of the model.

• Language: English
• Keywords: nonequilibrium statistical mechanics
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Author Accepted Manuscript
• Year: 2020
• Number of pages: Str. 062107-1-062107-16
• Numbering: Vol. 102, iss. 6
• PID: 20.500.12556/RUL-124297
• UDC: 536
• ISSN on article: 2470-0045
• DOI: 10.1103/PhysRevE.102.062107
• COBISS.SI-ID: 46993155
• Publication date in RUL: 14.01.2021

WILKINSON, Joseph W. P., KLOBAS, Katja, PROSEN, Tomaž and GARRAHAN, Juan P., 2020, Exact solution of the Floquet-PXP cellular automaton. Physical review [online]. 2020. Vol. 102, no. 6, p. 062107-1- 062107–16. [Accessed 14 April 2025]. DOI 10.1103/PhysRevE.102.062107. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=124297

Record is a part of a journal

• Title: Physical review
• Shortened title: Phys. rev., E
• Publisher: American Physical Society
• ISSN: 2470-0045
• COBISS.SI-ID: 2048366611

Secondary language

• Language: Slovenian
• Keywords: neravnovesna statistična mehanika

Projects

• Funder: EC - European Commission
• Funding programme: H2020
• Project number: 694544
• Name: Open Many-body Non-Equilibrium Systems
• Acronym: OMNES

• Funder: ARRS - Slovenian Research Agency
• Project number: P1-0402
• Name: Matematična fizika