Pilatowsky-Cameo Saúl, Chávez-Carlos Jorge, Bastarrachea-Magnani Miguel A, Stránský Pavel, Lerma-Hernández Sergio, Santos Lea F, Hirsch Jorge G
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apdo. Postal 70-543, C.P. 04510 CDMX, Mexico.
Department of Physics and Astronomy, Aarhus University, Ny Munkegade, DK-8000 Aarhus C, Denmark.
Phys Rev E. 2020 Jan;101(1-1):010202. doi: 10.1103/PhysRevE.101.010202.
Quantum chaos refers to signatures of classical chaos found in the quantum domain. Recently, it has become common to equate the exponential behavior of out-of-time order correlators (OTOCs) with quantum chaos. The quantum-classical correspondence between the OTOC exponential growth and chaos in the classical limit has indeed been corroborated theoretically for some systems and there are several projects to do the same experimentally. The Dicke model, in particular, which has a regular and a chaotic regime, is currently under intense investigation by experiments with trapped ions. We show, however, that for experimentally accessible parameters, OTOCs can grow exponentially also when the Dicke model is in the regular regime. The same holds for the Lipkin-Meshkov-Glick model, which is integrable and also experimentally realizable. The exponential behavior in these cases are due to unstable stationary points, not to chaos.
量子混沌是指在量子领域中发现的经典混沌的特征。最近，将超越时间序关联函数（OTOCs）的指数行为等同于量子混沌已变得很常见。在经典极限下，OTOC指数增长与混沌之间的量子-经典对应关系确实已在理论上得到了一些系统的证实，并且有几个项目正在进行相关的实验。特别是具有规则和混沌区域的迪克模型，目前正受到囚禁离子实验的深入研究。然而，我们表明，对于实验可及的参数，当迪克模型处于规则区域时，OTOCs也可以指数增长。对于可积且在实验上也可实现的利普金-梅什科夫-格利克模型也是如此。在这些情况下的指数行为是由于不稳定的驻点，而非混沌。
