Quantum systems, when interacting with their environments, may exhibit nonequilibrium states that are tempting to be interpreted as quantum analogs of chaotic attractors. However, different from the Hamiltonian case, the toolbox for quantifying dissipative quantum chaos remains limited. In particular, quantum generalizations of Lyapunov exponents, the main quantifiers of classical chaos, are established only within the framework of continuous measurements. We propose an alternative generalization based on the unraveling of quantum master equation into an ensemble of “quantum trajectories,” by using the so-called Monte Carlo wave-function method. We illustrate the idea with a periodically modulated open quantum dimer and demonstrate that the transition to quantum chaos matches the period-doubling route to chaos in the corresponding mean-field system.
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June 2019
Research Article|
June 28 2019
Quantum Lyapunov exponents beyond continuous measurements
I. I. Yusipov;
I. I. Yusipov
1
Department of Applied Mathematics, Lobachevsky University
, Nizhny Novgorod 603950, Russia
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O. S. Vershinina;
O. S. Vershinina
1
Department of Applied Mathematics, Lobachevsky University
, Nizhny Novgorod 603950, Russia
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S. Denisov;
S. Denisov
2
Department of Computer Science, Oslo Metropolitan University
, Oslo N-0130, Norway
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S. P. Kuznetsov;
S. P. Kuznetsov
3
Kotelnikovs Institute of Radio-Engineering and Electronics of RAS
, Saratov 410019, Russia
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M. V. Ivanchenko
M. V. Ivanchenko
1
Department of Applied Mathematics, Lobachevsky University
, Nizhny Novgorod 603950, Russia
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Chaos 29, 063130 (2019)
Article history
Received:
February 28 2019
Accepted:
June 10 2019
Citation
I. I. Yusipov, O. S. Vershinina, S. Denisov, S. P. Kuznetsov, M. V. Ivanchenko; Quantum Lyapunov exponents beyond continuous measurements. Chaos 1 June 2019; 29 (6): 063130. https://doi.org/10.1063/1.5094324
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