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

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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.

Keywords:quantum mechanics, quantum chaos, open quantum systems, nonlinear dynamics, statistical physics
Tipology:1.01 - Original Scientific Article
Organization:FMF - Faculty of Mathematics and Physics
Number of pages:str. 254101-1-254101-6
Numbering:Vol. 123, iss. 25
ISSN on article:0031-9007
DOI:10.1103/PhysRevLett.123.254101 Link is opened in a new window
COBISS.SI-ID:3395940 Link is opened in a new window
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Record is a part of a journal

Title:Physical review letters
Shortened title:Phys. rev. lett.
Publisher:American Physical Society
COBISS.SI-ID:1282575 This link opens in a new window

Document is financed by a project

Funder:EC - European Commission
Funding Programme:H2020
Project no.:694544
Name:Open many-body non-equilibrium systems

Funder:ARRS - Agencija za raziskovalno dejavnost Republike Slovenije (ARRS)
Project no.:P1-0402
Name:Matematična fizika

Secondary language

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

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