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Rule 54: exactly solvable model of nonequilibrium statistical mechanics
ID
Buča, Berislav
(
Author
),
ID
Klobas, Katja
(
Author
),
ID
Prosen, Tomaž
(
Author
)
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https://iopscience.iop.org/article/10.1088/1742-5468/ac096b
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Abstract
We review recent results on an exactly solvable model of nonequilibrium statistical mechanics, specifically the classical rule 54 reversible cellular automaton and some of its quantum extensions. We discuss the exact microscopic description of nonequilibrium dynamics as well as the equilibrium and nonequilibrium stationary states. This allows us to obtain a rigorous handle on the corresponding emergent hydrodynamic description, which is treated as well. Specifically, we focus on two different paradigms of rule 54 dynamics. Firstly, we consider a finite chain driven by stochastic boundaries, where we provide exact matrix product descriptions of the nonequilibrium steady state, most relevant decay modes, as well as the eigenvector of the tilted Markov chain yielding exact large deviations for a broad class of local and extensive observables. Secondly, we treat the explicit dynamics of macro-states on an infinite lattice and discuss exact closed form results for dynamical structure factor, multi-time-correlation functions and inhomogeneous quenches. Remarkably, these results prove that the model, despite its simplicity, behaves like a regular fluid with coexistence of ballistic (sound) and diffusive (heat) transport. Finally, we briefly discuss quantum interpretation of rule 54 dynamics and explicit results on dynamical spreading of local operators and operator entanglement.
Language:
English
Keywords:
statistical mechanics
,
non-equilibrium systems
,
cellular automata
,
thermalization
Typology:
1.01 - Original Scientific Article
Organization:
FMF - Faculty of Mathematics and Physics
Publication status:
Published
Publication version:
Author Accepted Manuscript
Year:
2021
Number of pages:
70 str.
Numbering:
Vol. 2021, art. no. ǂ074001
PID:
20.500.12556/RUL-130305
UDC:
536.9
ISSN on article:
1742-5468
DOI:
10.1088/1742-5468/ac096b
COBISS.SI-ID:
76119811
Publication date in RUL:
13.09.2021
Views:
936
Downloads:
90
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Record is a part of a journal
Title:
Journal of statistical mechanics
Shortened title:
J. stat. mech.
Publisher:
IOP Publishing
ISSN:
1742-5468
COBISS.SI-ID:
21517607
Secondary language
Language:
Slovenian
Keywords:
statistična mehanika
,
neravnovesni sistemi
,
celični avtomati
,
termalizacija
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
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