Chaos and ergodicity in extended quantum systems with noisy driving

Kos, Pavel (author), Bertini, Bruno (author), Prosen, Tomaž (author)

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.

• Language: English
• Keywords: statistical physics, nonlinear dynamics, quantum mechanics, quantum chaos
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2021
• Number of pages: Str. 190601-1-190601-7
• Numbering: Vol. 126, iss. 19
• PID: 20.500.12556/RUL-127107
• UDC: 530.145
• ISSN on article: 0031-9007
• DOI: 10.1103/PhysRevLett.126.190601
• COBISS.SI-ID: 63236355
• Publication date in RUL: 18.05.2021

Record is a part of a journal

• Title: Physical review letters
• Shortened title: Phys. rev. lett.
• Publisher: American Physical Society
• ISSN: 0031-9007
• COBISS.SI-ID: 1282575

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• 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

• Language: Slovenian
• Keywords: statistična fizika, nelinearna dinamika, kvantna mehanika, kvantni kaos

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