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Spectral statistics of non-Hermitian matrices and dissipative quantum chaos
Li, Jiachen (Avtor), Prosen, Tomaž (Avtor), Chan, Amos (Avtor)

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Izvleček
We propose a measure, which we call the dissipative spectral form factor (DSFF), to characterize the spectral statistics of non-Hermitian (and nonunitary) matrices. We show that DSFF successfully diagnoses dissipative quantum chaos and reveals correlations between real and imaginary parts of the complex eigenvalues up to arbitrary energy scale (and timescale). Specifically, we provide the exact solution of DSFF for the complex Ginibre ensemble (GinUE) and for a Poissonian random spectrum (Poisson) as minimal models of dissipative quantum chaotic and integrable systems, respectively. For dissipative quantum chaotic systems, we show that the DSFF exhibits an exact rotational symmetry in its complex time argument $\tau$. Analogous to the spectral form factor (SFF) behavior for Gaussian unitary ensemble, the DSFF for GinUE shows a “dip-ramp-plateau” behavior in |$\tau$|: the DSFF initially decreases, increases at intermediate timescales, and saturates after a generalized Heisenberg time, which scales as the inverse mean level spacing. Remarkably, for large matrix size, the “ramp” of the DSFF for GinUE increases quadratically in |$\tau$|, in contrast to the linear ramp in the SFF for Hermitian ensembles. For dissipative quantum integrable systems, we show that the DSFF takes a constant value, except for a region in complex time whose size and behavior depend on the eigenvalue density. Numerically, we verify the above claims and additionally show that the DSFF for real and quaternion real Ginibre ensembles coincides with the GinUE behavior, except for a region in the complex time plane of measure zero in the limit of large matrix size. As a physical example, we consider the quantum kicked top model with dissipation and show that it falls under the Ginibre universality class and Poisson as the “kick” is switched on or off. Lastly, we study spectral statistics of ensembles of random classical stochastic matrices or Markov chains and show that these models again fall under the Ginibre universality class.

Jezik:Angleški jezik
Ključne besede:quantum mechanics, quantum chaos, statistical physics
Tipologija:1.01 - Izvirni znanstveni članek
Organizacija:FMF - Fakulteta za matematiko in fiziko
Leto izida:2021
Št. strani:Str. 170602-1-170602-7
Številčenje:Vol. 127, iss. 17
UDK:536.93
ISSN pri članku:0031-9007
DOI:10.1103/PhysRevLett.127.170602 Povezava se odpre v novem oknu
COBISS.SI-ID:81850115 Povezava se odpre v novem oknu
Število ogledov:66
Število prenosov:59
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Gradivo je del revije

Naslov:Physical review letters
Skrajšan naslov:Phys. rev. lett.
Založnik:American Physical Society
ISSN:0031-9007
COBISS.SI-ID:1282575 Povezava se odpre v novem oknu

Gradivo je financirano iz projekta

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 (ARRS)
Številka projekta:P1-0402
Naslov:Matematična fizika

Sekundarni jezik

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

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