Quantum and Classical Lyapunov Exponents in Atom-Field Interaction Systems
Jorge Chávez-Carlos,B. López-del-Carpio,Miguel A. Bastarrachea-Magnani,Pavel Stránský,Sergio Lerma-Hernández,Lea F. Santos,Jorge G. Hirsch +6 more
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TLDR
The exponential growth of the out-of-time-ordered correlator (OTOC) has been proposed as a quantum signature of classical chaos and is studied in the Dicke model, where two-level atoms cooperatively interact with a quantized radiation field.Abstract:
The exponential growth of the out-of-time-ordered correlator (OTOC) has been proposed as a quantum signature of classical chaos. The growth rate is expected to coincide with the classical Lyapunov exponent. This quantum-classical correspondence has been corroborated for the kicked rotor and the stadium billiard, which are one-body chaotic systems. The conjecture has not yet been validated for realistic systems with interactions. We make progress in this direction by studying the OTOC in the Dicke model, where two-level atoms cooperatively interact with a quantized radiation field. For parameters where the model is chaotic in the classical limit, the OTOC increases exponentially in time with a rate that closely follows the classical Lyapunov exponent.read more
Citations
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Unifying scrambling, thermalization and entanglement through measurement of fidelity out-of-time-order correlators in the Dicke model.
TL;DR: It is demonstrated that fidelity out-of-time-order correlators (FOTOCs) can elucidate connections between scrambling, entanglement, ergodicity and quantum chaos (butterfly effect) and establish quantitative relationships between experimentally-measureable correlators, the Rényi entropy and Lyapunov exponents in the Dicke model.
Journal ArticleDOI
Positive quantum Lyapunov exponents in experimental systems with a regular classical limit
Saúl Pilatowsky-Cameo,Jorge Chávez-Carlos,Miguel A. Bastarrachea-Magnani,Pavel Stránský,Sergio Lerma-Hernández,Lea F. Santos,Jorge G. Hirsch +6 more
TL;DR: In this article, it was shown that for experimentally accessible parameters, OTOCs can grow exponentially also when the Dicke model is in the regular regime, and the same holds for the Lipkin-Meshkov-Glick model, which is integrable and also experimentally realizable.
Journal ArticleDOI
Quantum versus classical many-body batteries
Gian Marcello Andolina,Gian Marcello Andolina,Maximilian Keck,Andrea Mari,Vittorio Giovannetti,Marco Polini +5 more
TL;DR: In this article, the authors studied three examples of quantum-mechanical many-body batteries with rigorous classical analogs and found that the answer is model dependent and depends on the value of the coupling constant that controls the interaction between the charger and the battery itself.
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Does Scrambling Equal Chaos
TL;DR: In this article, the authors show that scrambling can simply result from the presence of unstable fixed points in phase space, even in a classically integrable model, and derive a lower bound on the Lyapunov exponent, which depends only on local properties of such fixed points.
Journal ArticleDOI
Unifying fast scrambling, thermalization and entanglement through the measurement of FOTOCs in the Dicke model
TL;DR: In this paper, a family of fidelity out-of-time-order correlators (FOTOCs) is proposed to quantify fast scrambling, determine bounds on quantum information processing and to identify possible candidates of black hole analogs in controllable quantum systems.
References
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