Pavel Kos (Author), Bruno Bertini (Author), Tomaž Prosen (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.

Keywords

statistična fizika;nelinearna dinamika;kvantna mehanika;kvantni kaos;statistical physics;nonlinear dynamics;quantum mechanics;quantum chaos;

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UL FMF - Faculty of Mathematics and Physics
UDC: 530.145
COBISS: 63236355 Link will open in a new window
ISSN: 0031-9007
Views: 266
Downloads: 100
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Other data

Secondary language: Slovenian
Secondary keywords: statistična fizika;nelinearna dinamika;kvantna mehanika;kvantni kaos;
Type (COBISS): Article
Pages: str. 190601-1-190601-7
Volume: ǂVol. ǂ126
Issue: ǂiss. ǂ19
Chronology: 2021
DOI: 10.1103/PhysRevLett.126.190601
ID: 12910844