Journal article
Universal Signature from Integrability to Chaos in Open Quantum Systems
Mario Kieburg, Gernot Akemann, Adam Mielke, Tomaz Prosen
Physical Review Letters | American Physical Society | Published : 2019
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 β∈[0,2]. Here, β=0 yields the two-dimensional Poisson distribution, matching the integrable limit of the system, and β=2 equals the distribution obtained from the complex Ginibre ensemble, describing the fully chaotic limit. Our findings generalize the..
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Awarded by Horizon 2020 Framework Programme
Funding Acknowledgements
This work was partly funded by the Wallenberg foundation (G. A.), the German Science Foundation DFG within CRC1283, "Taming uncertainty and profiting from randomness and low regularity in analysis, stochastics, and their applications"(G. A. and M. K.), and within IRTG2235, "Searching for the regular in the irregular: Analysis of singular and random systems" (A. M.), by the European Research Council under Advanced Grant No. 694544-OMNES (T. P.), and by the Slovenian Research Agency (ARRS) under Program No. P1-0402 (T. P.). Support from the Simons Center for Geometry and Physics, Stony Brook University, where part of this work was completed (G. A. and M. K.), is gratefully acknowledged, as are the fruitful discussions with Maurice Duits (G. A.).