### Universal Signature from Integrability to Chaos in Dissipative Open Quantum Systems

Akemann G, Kieburg M, Mielke A, Prosen T (2019)
arXiv:1910.03520.

Preprint| Englisch

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Autor*in
Akemann, GernotUniBi; Kieburg, Mario; Mielke, AdamUniBi; Prosen, Tomaz
Abstract / Bemerkung
We study the transition between integrable and chaotic behaviour 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 generalise 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.
Erscheinungsjahr
2019
Zeitschriftentitel
arXiv:1910.03520
Page URI
https://pub.uni-bielefeld.de/record/2939392

### Zitieren

Akemann G, Kieburg M, Mielke A, Prosen T. Universal Signature from Integrability to Chaos in Dissipative Open Quantum Systems. arXiv:1910.03520. 2019.
Akemann, G., Kieburg, M., Mielke, A., & Prosen, T. (2019). Universal Signature from Integrability to Chaos in Dissipative Open Quantum Systems. arXiv:1910.03520
Akemann, G., Kieburg, M., Mielke, A., and Prosen, T. (2019). Universal Signature from Integrability to Chaos in Dissipative Open Quantum Systems. arXiv:1910.03520.
Akemann, G., et al., 2019. Universal Signature from Integrability to Chaos in Dissipative Open Quantum Systems. arXiv:1910.03520.
G. Akemann, et al., “Universal Signature from Integrability to Chaos in Dissipative Open Quantum Systems”, arXiv:1910.03520, 2019.
Akemann, G., Kieburg, M., Mielke, A., Prosen, T.: Universal Signature from Integrability to Chaos in Dissipative Open Quantum Systems. arXiv:1910.03520. (2019).
Akemann, Gernot, Kieburg, Mario, Mielke, Adam, and Prosen, Tomaz. “Universal Signature from Integrability to Chaos in Dissipative Open Quantum Systems”. arXiv:1910.03520 (2019).

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### Quellen

arXiv: 1910.03520