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Complex spacing ratios: a signature of dissipative quantum chaos
ID
Sá, Lucas
(
Avtor
),
ID
Ribeiro, Pedro
(
Avtor
),
ID
Prosen, Tomaž
(
Avtor
)
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URL - Izvorni URL, za dostop obiščite
https://journals.aps.org/prx/abstract/10.1103/PhysRevX.10.021019
Galerija slik
Izvleček
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
Število ogledov:
1318
Število prenosov:
341
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Objavi na:
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
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