Universal signature from integrability to chaos in dissipative open quantum systems
ID Akemann, Gernot (Author), ID Kieburg, Mario (Author), ID Mielke, Adam (Author), ID Prosen, Tomaž (Author)

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Abstract
We study the transition between integrable and chaotic behavior in dissipative open quantum systems, exemplified by a boundary driven quantum spin chain. The repulsion between the complex eigenvalues of the corresponding Liouville operator in radial distance $s$ is used as a universal measure. The corresponding level spacing distribution is well fitted by that of a static two-dimensional Coulomb gas with harmonic potential at inverse temperature $\beta \in [0,2]$. Here, $\beta=0$ yields the two-dimensional Poisson distribution, matching the integrable limit of the system, and $\beta=2$ equals the distribution obtained from the complex Ginibre ensemble, describing the fully chaotic limit. Our findings generalize the results of Grobe, Haake, and Sommers, who derived a universal cubic level repulsion for small spacings $s$. We collect mathematical evidence for the universality of the full level spacing distribution in the fully chaotic limit at $\beta=2$. It holds for all three Ginibre ensembles of random matrices with independent real, complex, or quaternion matrix elements.

Language: English quantum mechanics, quantum chaos, open quantum systems, nonlinear dynamics, statistical physics 1.01 - Original Scientific Article FMF - Faculty of Mathematics and Physics 2019 Published Postprint, final article version, accepted into publication Str. 254101-1-254101-6 Vol. 123, iss. 25 20.500.12556/RUL-113303 530.182 0031-9007 10.1103/PhysRevLett.123.254101 3395940 19.12.2019 654 488 Kopiraj citat AddThis uses cookies that require your consent. Edit consent...

## Record is a part of a journal

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

## Secondary language

Language: Slovenian kvantna mehanika, kvantni kaos, odprti kvantni sistemi, nelinearna dinamika, statistična fizika

## Projects

Funder: EC - European Commission H2020 694544 Open many-body non-equilibrium systems OMNES

Funder: ARRS - Agencija za raziskovalno dejavnost Republike Slovenije P1-0402 Matematična fizika

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