Matrix product state of multi-time correlations

Klobas, Katja (author), Vanicat, Matthieu (author), Garrahan, Juan P. (author), Prosen, Tomaž (author)

For an interacting spatio-temporal lattice system we introduce a formal way of expressing multi-time correlation functions of local observables located at the same spatial point with a time state, i.e. a statistical distribution of configurations observed along a time lattice. Such a time state is defined with respect to a particular equilibrium state that is invariant under space and time translations. The concept is developed within the rule 54 reversible cellular automaton, for which we explicitly construct a matrix product form of the time state, with matrices that act on the three-dimensional auxiliary space. We use the matrix-product state to express equal-space time-dependent density-density correlation function, which, for special maximum-entropy values of equilibrium parameters, agrees with the previous results. Additionally, we obtain an explicit expression for the probabilities of observing all multi-time configurations, which enables us to study distributions of times between consecutive excitations and prove the absence of decoupling of timescales in the rule 54 model.

• Language: English
• 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: 17 str.
• Numbering: Vol. 53, art. no. 335001
• PID: 20.500.12556/RUL-118044
• UDC: 51-7:53
• ISSN on article: 1751-8113
• DOI: 10.1088/1751-8121/ab8c62
• COBISS.SI-ID: 25249283
• Publication date in RUL: 17.08.2020

Record is a part of a journal

• Title: Journal of physics : Mathematical and theoretical
• Shortened title: J. phys., A, Math. theor.
• Publisher: IOP Publishing
• ISSN: 1751-8113
• COBISS.SI-ID: 3692314

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