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

Povzetek

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.

Ključne besede

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

Podatki

Jezik: Angleški jezik
Leto izida:
Tipologija: 1.01 - Izvirni znanstveni članek
Organizacija: UL FMF - Fakulteta za matematiko in fiziko
UDK: 530.145
COBISS: 23748355 Povezava se bo odprla v novem oknu
ISSN: 2160-3308
Št. ogledov: 451
Št. prenosov: 195
Ocena: 0 (0 glasov)
Metapodatki: JSON JSON-RDF JSON-LD TURTLE N-TRIPLES XML RDFA MICRODATA DC-XML DC-RDF RDF

Ostali podatki

Sekundarni jezik: Slovenski jezik
Sekundarne ključne besede: nelinearna dinamika;statistična fizika;kvantni kaos;
Strani: str. 021019-1-021019-23
Letnik: ǂVol. ǂ10
Zvezek: ǂiss. ǂ2
Čas izdaje: 2020
DOI: 10.1103/PhysRevX.10.021019
ID: 11922574