20.500.12556/RUL-117814 Complex spacing ratios: a signature of dissipative quantum chaos 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. nonlinear dynamics statistical physics quantum chaos nelinearna dinamika statistična fizika kvantni kaos true false false Angleški jezik Slovenski jezik Neznano 2020-07-28 09:11:03 2020-07-28 09:11:05 2022-08-30 04:00:23 0000-00-00 00:00:00 2020 0 0 Str. 021019-1-021019-23 iss. 2 Vol. 10 2020 0000-00-00 PostprintKoncna Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 530.145 2160-3308 10.1103/PhysRevX.10.021019 23748355 19686152 RAZ_Sa_Lucas_2020.pdf RAZ_Sa_Lucas_2020.pdf 1 8DDA26DD96815EDEF0440C0295CAA4DD e4e9be9eb790b3717fa2a6e44cde48b3302f414ee6e110e5525475b29ddabab9 44cb5808-a1b9-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=131717 https://journals.aps.org/prx/abstract/10.1103/PhysRevX.10.021019 1 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=140293 Fakulteta za matematiko in fiziko 0 0 0