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Time-dependent matrix product ansatz for interacting reversible dynamics
ID Klobas, Katja (Author), ID Medenjak, Marko (Author), ID Prosen, Tomaž (Author), ID Vanicat, Matthieu (Author)

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Abstract
We present an explicit time-dependent matrix product ansatz (tMPA), which describes the time-evolution of any local observable in an interacting and deterministic lattice gas, specifically for the rule 54 reversible cellular automaton of Bobenko et al. (Commun Math Phys 158(1):127, 1993. https://doi.org/10.1007/BF02097234). Our construction is based on an explicit solution of real-space real-time inverse scattering problem. We consider two applications of this tMPA. Firstly, we provide the first exact and explicit computation of the dynamic structure factor in an interacting deterministic model, and secondly, we solve the extremal case of the inhomogeneous quench problem, where a semi-infinite lattice in the maximum entropy state is joined with an empty semi-infinite lattice. Both of these exact results rigorously demonstrate a coexistence of ballistic and diffusive transport behaviour in the model, as expected for normal fluids.

Language:English
Typology:1.01 - Original Scientific Article
Organization:FMF - Faculty of Mathematics and Physics
Publication status:Published
Publication version:Author Accepted Manuscript
Year:2019
Number of pages:Str. 651-688
Numbering:Vol. 371, iss. 2
PID:20.500.12556/RUL-113032 This link opens in a new window
UDC:51-7:53
ISSN on article:0010-3616
DOI:10.1007/s00220-019-03494-5 This link opens in a new window
COBISS.SI-ID:3367012 This link opens in a new window
Publication date in RUL:29.11.2019
Views:1433
Downloads:542
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Record is a part of a journal

Title:Communications in Mathematical Physics
Shortened title:Commun. Math. Phys.
Publisher:Springer-Verlag
ISSN:0010-3616
COBISS.SI-ID:25250304 This link opens in a new window

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:P1-0044
Name:Teorija trdnih snovi in statistična fizika

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

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