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 quantum mechanics, quantum chaos, statistical physics 1.01 - Izvirni znanstveni članek FMF - Fakulteta za matematiko in fiziko 2021 Str. 170602-1-170602-7 Vol. 127, iss. 17 536.93 0031-9007 10.1103/PhysRevLett.127.170602 81850115 66 59 (0 glasov) Ocenjevanje je dovoljeno samo prijavljenim uporabnikom. AddThis uporablja piškotke, za katere potrebujemo vaše privoljenje.Uredi privoljenje...

Naslov: Physical review letters Phys. rev. lett. American Physical Society 0031-9007 1282575

## Gradivo je financirano iz projekta

Financer: EC - European Commission H2020 694544 Open Many-body Non-Equilibrium Systems OMNES

Financer: ARRS - Agencija za raziskovalno dejavnost Republike Slovenije (ARRS) P1-0402 Matematična fizika

## Sekundarni jezik

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

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