Complex spacing ratios: a signature of dissipative quantum chaos

Sá, Lucas (avtor), Ribeiro, Pedro (avtor), Prosen, Tomaž (avtor)

We introduce a complex-plane generalization of the consecutive level-spacing ratio distribution used to distinguish regular from chaotic quantum spectra. Our approach features the distribution of complex-valued ratios between nearest- and next-to-nearest-neighbor spacings. We show that this quantity can successfully detect the chaotic or regular nature of complex-valued spectra, which is done in two steps. First, we show that, if eigenvalues are uncorrelated, the distribution of complex spacing ratios is flat within the unit circle, whereas random matrices show a strong angular dependence in addition to the usual level repulsion. The universal fluctuations of Gaussian unitary and Ginibre unitary universality classes in the large-matrix-size limit are shown to be well described by Wigner-like surmises for small-size matrices with eigenvalues on the circle and on the two-torus, respectively. To study the latter case, we introduce the toric unitary ensemble, characterized by a flat joint eigenvalue distribution on the two-torus. Second, we study different physical situations where non-Hermitian matrices arise: dissipative quantum systems described by a Lindbladian, nonunitary quantum dynamics described by non-Hermitian Hamiltonians, and classical stochastic processes. We show that known integrable models have a flat distribution of complex spacing ratios, whereas generic cases, expected to be chaotic, conform to random matrix theory predictions. Specifically, we are able to clearly distinguish chaotic from integrable dynamics in boundary-driven dissipative spin-chain Liouvillians and in the classical asymmetric simple exclusion process and to differentiate localized from delocalized regimes in a non-Hermitian disordered many-body system.

• Jezik: Angleški jezik
• Ključne besede: nonlinear dynamics, statistical physics, quantum chaos
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Recenzirani rokopis
• Leto izida: 2020
• Št. strani: Str. 021019-1-021019-23
• Številčenje: Vol. 10, iss. 2
• PID: 20.500.12556/RUL-117814
• UDK: 530.145
• ISSN pri članku: 2160-3308
• DOI: 10.1103/PhysRevX.10.021019
• COBISS.SI-ID: 23748355
• Datum objave v RUL: 28.07.2020

Gradivo je del revije

• Naslov: Physical review
• Skrajšan naslov: Phys. rev., X
• Založnik: American Physical Society
• ISSN: 2160-3308
• COBISS.SI-ID: 19686152

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: 28.07.2020

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: nelinearna dinamika, statistična fizika, 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
• Program financ.: P1-0402
• Številka projekta: P1-0402
• Naslov: Matematična fizika