Bergamasco Pablo D, Carlo Gabriel G, Rivas Alejandro M F
Departamento de Física, CNEA, Libertador 8250, (C1429BNP) Buenos Aires, Argentina.
Departamento de Física, CNEA, CONICET, Libertador 8250, (C1429BNP) Buenos Aires, Argentina.
Phys Rev E. 2023 Aug;108(2-1):024208. doi: 10.1103/PhysRevE.108.024208.
The out-of-time order correlator (OTOC) has been widely studied in closed quantum systems. However, there are very few studies for open systems and they are mainly focused on isolating the effects of scrambling from those of decoherence. Adopting a different point of view, we study the interplay between these two processes. This proves crucial in order to explain the OTOC behavior when a phase space contracting dissipation is present, ubiquitous not only in real life quantum devices but in the dynamical systems area. The OTOC decay rate is closely related to the classical Lyapunov exponent-with some differences-and more sensitive in order to distinguish the chaotic from the regular behavior than other measures. On the other hand, it is revealed as a generally simple function of the longest lived eigenvalues of the quantum evolution operator. We find no simple connection with the Ruelle-Pollicott resonances, but by adding Gaussian noise of ℏ_{eff} size to the classical system we recover the OTOC decay rate, which is a consequence of the correspondence principle put forward in Phys. Rev. Lett. 108, 210605 (2012)10.1103/PhysRevLett.108.210605 and Phys. Rev. E 99, 042214 (2019)10.1103/PhysRevE.99.042214.
非即时序关联函数（OTOC）在封闭量子系统中已得到广泛研究。然而，对于开放系统的研究却非常少，且主要集中于将量子混沌效应与退相干效应区分开来。我们从不同的角度出发，研究这两个过程之间的相互作用。事实证明，这对于解释存在相空间收缩耗散时的OTOC行为至关重要，这种耗散不仅在实际的量子器件中普遍存在，在动力系统领域也是如此。OTOC衰减率与经典李雅普诺夫指数密切相关——存在一些差异——并且相比于其他度量，它在区分混沌行为和规则行为方面更为敏感。另一方面，它表现为量子演化算符最长寿命本征值的一个通常较为简单的函数。我们发现它与吕埃勒 - 波利科特共振没有简单的联系，但通过向经典系统添加有效普朗克常数大小的高斯噪声，我们恢复了OTOC衰减率，这是《物理评论快报》108, 210605 (2012)10.1103/PhysRevLett.108.210605和《物理评论E》99, 042214 (2019)10.1103/PhysRevE.99.042214中提出的对应原理的一个结果。
