近日，俄罗斯量子中心的Evgeny Polyakov与Nataliya Arefyeva合作并取得一项新进展。经过不懈努力，他们利用退相干历史的熵探测量子混沌。相关研究成果已于2024年6月3日在国际知名学术期刊《物理评论A》上发表。
据悉，量子混沌是上个世纪开始研究的一种现象，至今仍没有一个严谨的认识。根据对应原理，导致经典水平混沌动力学的系统性质也必须存在于底层量子系统中。在经典情况下，附近轨迹在时间上的指数散度是用李雅普诺夫指数来描述的。然而，在量子情况下，严格来说，由于没有轨迹，对混沌的类似描述是不可能的。有不同的方法来补救这种情况，但量子混沌的普遍标准是缺乏的。人们提出了一个量子混沌的定义，以一种类似于传统的方式，使用退相干历史作为轨迹的量子模拟。
为此，该研究团队考虑了开放量子受激顶部与环境(玻色子浴)相互作用的模型，并阐明了这一思想。在这个模型中，环境扮演了记录量子轨迹的角色。对于经典层面的受激顶部模型而言，随着受激强度的变化，可积与混沌状态之间会发生交叉。研究人员证明，在这一模型中，无论是在可积状态还是混沌状态下，退相干历史的熵的产生方式都截然不同。这一发现揭示了量子轨迹系综的熵可以作为量子混沌的一个重要特征。
附：英文原文
Title: Probing quantum chaos with the entropy of decoherent histories
Author: Evgeny Polyakov, Nataliya Arefyeva
Issue&Volume: 2024/06/03
Abstract: Quantum chaos, a phenomenon that began to be studied in the last century, still does not have a rigorous understanding. By virtue of the correspondence principle, the properties of the system that lead to chaotic dynamics at the classical level must also be present in the underlying quantum system. In the classical case, the exponential divergence of nearby trajectories in time is described in terms of the Lyapunov exponent. However, in the quantum case, a similar description of chaos is, strictly speaking, impossible due to the absence of trajectories. There are different approaches to remedy this situation, but the universal criterion of quantum chaos is absent. We propose a quantum chaos definition in a manner similar to the classical one using decoherent histories as a quantum analog of trajectories. For this purpose, we consider the model of an open quantum kicked top interacting with the environment, which is a bosonic bath, and illustrate this idea. Here, the environment plays the role of a trajectory-recording device. For the kicked-top model at the classical level, depending on the kick strength, crossover occurs between the integrable and chaotic regimes. We show that for such a model, the production of entropy of decoherent histories is radically different in integrable and chaotic regimes. Thus, the entropy of an ensemble of quantum trajectories can be used as a signature of quantum chaos.
DOI: 10.1103/PhysRevA.109.062204
Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.109.062204
来源：科学网小柯机器人