孤立量子系统的动力学弛豫及热化机制

Thermalization of an isolated quantum system lies at the foundation of quantum statistical mechanics. Thermalization in an isolated system is a process where an arbitrary initial state relaxes to the equilibrium state of the microcanonical ensemble. For a classical system, thermalization can be induced by chaos as chaos guaranttees ergodicity. In contrast, quantum system is inherently linear and has no chaos in the classical sense. As a result, there is still no consensus whether an isolated quantum system can thermalize. In recent years, ultracold atoms have provided an ideal experimental platform to study isolated quantum systems. This development has re-ignited the wide spread interests in the thermalization of an isolated quantum systems.In this project, by focusing the universality of all the quantum chaotic systems, we study a quantum chaotic billiard system to find common features in quantum chaotic dynamics and reveal the hidden relations betweeen quantum chaos, dynamical relaxation and quantum thermalizaiton.

)：孤立量子系统的动力学弛豫和热化是建构量子统计物理的重要基石。热化是指系统从任意初态经过长时演化弛豫到微正则系综所描述的热力学平衡态的过程。在孤立经典系统中,热化所需的各态历经由混沌保证；然而量子系统是内禀线性系统,热化必与经典系统完全不同,其机制至今远无定论。近年来,具有高度孤立性和实验可操控性的超冷原子系统的出现为从根本上探索量子混沌和量子热化的内在联系提供了近乎完美的实验平台,并促使关于孤立量子系统的非平衡动力学和量子热化的研究成为一个新兴前沿课题。本项目着重于量子混沌系统的普适共性,以在超冷原子实验中可以实现的孤立二维波状量子弹球混沌系统(quantum billiard)为例,系统地研究混沌在量子体系定态表征和动力学演化上的规律, 并在此基础上阐明量子混沌、动力学驰豫以及量子热化的内在联系。

本人在项目资助下深入研究了孤立量子系统的热化问题，并且取得了实质性进展。我们证明了一个新的量子H定理，定义了一个新的量子熵，揭示了热力学第二定律的量子起源，重新认识了量子体系的各态历经和混合(mixing)。我们的理论结果表明，我们可以在不做任何假设的基础上建立量子微正则系综，奠定量子统计力学的基础。我们还和实验组合作在BEC观察到了量子平衡态的形成。