Matrix product state of multi-time correlations

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

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.

• Jezik: Angleški jezik
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Recenzirani rokopis
• Leto izida: 2020
• Št. strani: 17 str.
• Številčenje: Vol. 53, art. no. 335001
• PID: 20.500.12556/RUL-118044
• UDK: 51-7:53
• ISSN pri članku: 1751-8113
• DOI: 10.1088/1751-8121/ab8c62
• COBISS.SI-ID: 25249283
• Datum objave v RUL: 17.08.2020

KLOBAS, Katja, VANICAT, Matthieu, GARRAHAN, Juan P. in PROSEN, Tomaž, 2020, Matrix product state of multi-time correlations. Journal of physics : Mathematical and theoretical [na spletu]. 2020. Vol. 53, no. 335001. [Dostopano 4 april 2025]. DOI 10.1088/1751-8121/ab8c62. Pridobljeno s: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=slv&id=118044

Gradivo je del revije

• Naslov: Journal of physics : Mathematical and theoretical
• Skrajšan naslov: J. phys., A, Math. theor.
• Založnik: IOP Publishing
• ISSN: 1751-8113
• COBISS.SI-ID: 3692314

Projekti

• Financer: EC - European Commission
• Program financ.: H2020
• Številka projekta: 694544
• Naslov: Open Many-body Non-Equilibrium Systems
• Akronim: OMNES

• Financer: ARRS - Agencija za raziskovalno dejavnost Republike Slovenije
• Številka projekta: P1-0402
• Naslov: Matematična fizika