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

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 str. 254101-1-254101-6 Vol. 123, iss. 25 530.182 0031-9007 10.1103/PhysRevLett.123.254101 3395940 187 175 (0 votes) Voting is allowed only to logged in users. 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

## Document is financed by a project

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

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

## Secondary language

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