Chaos and ergodicity in extended quantum systems with noisy driving
ID Kos, Pavel (Author), ID Bertini, Bruno (Author), ID Prosen, Tomaž (Author)

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We study the time-evolution operator in a family of local quantum circuits with random fields in a fixed direction. We argue that the presence of quantum chaos implies that at large times the time-evolution operator becomes effectively a random matrix in the many-body Hilbert space. To quantify this phenomenon, we compute analytically the squared magnitude of the trace of the evolution operator—the generalized spectral form factor—and compare it with the prediction of random matrix theory. We show that for the systems under consideration, the generalized spectral form factor can be expressed in terms of dynamical correlation functions of local observables in the infinite temperature state, linking chaotic and ergodic properties of the systems. This also provides a connection between the many-body Thouless time $\tau_{th}$—the time at which the generalized spectral form factor starts following the random matrix theory prediction—and the conservation laws of the system. Moreover, we explain different scalings of $\tau_{th}$ with the system size observed for systems with and without the conservation laws.

Keywords:statistical physics, nonlinear dynamics, quantum mechanics, quantum chaos
Work type:Article (dk_c)
Typology:1.01 - Original Scientific Article
Organization:FMF - Faculty of Mathematics and Physics
Publication status in journal:Published
Article version:Publisher's version of article
Number of pages:Str. 190601-1-190601-7
Numbering:Vol. 126, iss. 19
PID:20.500.12556/RUL-127107 This link opens in a new window
ISSN on article:0031-9007
DOI:10.1103/PhysRevLett.126.190601 This link opens in a new window
COBISS.SI-ID:63236355 This link opens in a new window
Publication date in RUL:18.05.2021
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Record is a part of a journal

Title:Physical review letters
Shortened title:Phys. rev. lett.
Publisher:American Physical Society
COBISS.SI-ID:1282575 This link opens in a new window


License:CC BY 4.0, Creative Commons Attribution 4.0 International
Description:This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.
Licensing start date:10.05.2021

Secondary language

Keywords:statistična fizika, nelinearna dinamika, kvantna mehanika, kvantni kaos


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

Funder:ARRS - Agencija za raziskovalno dejavnost Republike Slovenije
Project number:P1-0402
Name:Matematična fizika

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