Chaos and ergodicity in extended quantum systems with noisy driving

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

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.

• Jezik: Angleški jezik
• Ključne besede: statistical physics, nonlinear dynamics, quantum mechanics, quantum chaos
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2021
• Št. strani: Str. 190601-1-190601-7
• Številčenje: Vol. 126, iss. 19
• PID: 20.500.12556/RUL-127107
• UDK: 530.145
• ISSN pri članku: 0031-9007
• DOI: 10.1103/PhysRevLett.126.190601
• COBISS.SI-ID: 63236355
• Datum objave v RUL: 18.05.2021

Gradivo je del revije

• Naslov: Physical review letters
• Skrajšan naslov: Phys. rev. lett.
• Založnik: American Physical Society
• ISSN: 0031-9007
• COBISS.SI-ID: 1282575

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.
• Začetek licenciranja: 10.05.2021

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: statistična fizika, nelinearna dinamika, kvantna mehanika, kvantni kaos

Projekti

• Financer: EC - European Commission
• Program financ.: H2020
• Številka projekta: 694544
• Naslov: Open Many-body Non-Equilibrium Systems
• Akronim: OMNES

• Financer: ARRS - Agencija za raziskovalno dejavnost Republike Slovenije
• Številka projekta: P1-0402
• Naslov: Matematična fizika