Gernot Akemann (Author), Mario Kieburg (Author), Adam Mielke (Author), Tomaž Prosen (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.

Keywords

kvantna mehanika;kvantni kaos;odprti kvantni sistemi;nelinearna dinamika;statistična fizika;quantum mechanics;quantum chaos;open quantum systems;nonlinear dynamics;statistical physics;

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UL FMF - Faculty of Mathematics and Physics
UDC: 530.182
COBISS: 3395940 Link will open in a new window
ISSN: 0031-9007
Views: 588
Downloads: 466
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Other data

Secondary language: Slovenian
Secondary keywords: kvantna mehanika;kvantni kaos;odprti kvantni sistemi;nelinearna dinamika;statistična fizika;
Pages: str. 254101-1-254101-6
Volume: ǂVol. ǂ123
Issue: ǂiss. ǂ25
Chronology: 2019
DOI: 10.1103/PhysRevLett.123.254101
ID: 11344507