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

Abstract
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 statistical physics, nonlinear dynamics, quantum mechanics, quantum chaos Article (dk_c) 1.01 - Original Scientific Article FMF - Faculty of Mathematics and Physics 2021 Published Publisher's version of article Str. 190601-1-190601-7 Vol. 126, iss. 19 20.500.12556/RUL-127107 530.145 0031-9007 10.1103/PhysRevLett.126.190601 63236355 18.05.2021 314 110 Kopiraj citat AddThis uses cookies that require your consent. Edit consent...

## Record is a part of a journal

Title: Physical review letters Phys. rev. lett. American Physical Society 0031-9007 1282575

## Licences

License: CC BY 4.0, Creative Commons Attribution 4.0 International http://creativecommons.org/licenses/by/4.0/ 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. 10.05.2021

## Secondary language

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

## Projects

Funder: EC - European Commission H2020 694544 Open Many-body Non-Equilibrium Systems OMNES

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

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