周期性驱动系统的动力学可以是完全稳定的，其时间演化由具有非厄米哈密顿量的薛定谔方程控制。这一发现是最近才得到的，并将通过这项工作中发现的许多精确解得到加强。本研究的主要目的是探讨周期驱动稳定的非厄米特系统的绝热跟随动力学。我们专注于特殊的行为，稳定的循环（Floquet）国家在缓慢驾驶的限制。研究发现，稳定的循环态可以表现为直观预期的以下瞬时本征态，或表现出分段绝热以下瞬时本征态之间的突然切换。我们的目标是在各种不同的驾驶场景下覆盖广泛的非厄米系统。我们系统地分析了突然开关行为的普遍路线。也就是说，在我们的渐近分析的解决方案的临界指数的符号变化总是被发现的基本机制，以确定如果绝热以下的动力学是平凡的或分段的。因此，这项工作大大扩展了我们对同一主题的早期研究[Gong和Wang，Phys. Rev. A 97，052126（2018）]，并将激发对非厄米系统的更多兴趣。
英文摘要：
The dynamics of a periodically driven system whose time evolution is governed by the Schrödinger equation with non-Hermitian Hamiltonians can be perfectly stable. This finding was only obtained very recently and will be enhanced by many exact solutions discovered in this work. The main concern of this study is to investigate the adiabatic following dynamics in such non-Hermitian systems stabilized by periodic driving. We focus on the peculiar behaviour of stable cyclic (Floquet) states in the slow-driving limit. It is found that the stable cyclic states can either behave as intuitively expected by following instantaneous eigenstates, or exhibit piecewise adiabatic following by sudden-switching between instantaneous eigenstates. We aim to cover broad categories of non-Hermitian systems under a variety of different driving scenarios. We systematically analyse the sudden-switch behaviour by a universal route. That is, the sign change of the critical exponent in our asymptotic analysis of the solutions is always found to be the underlying mechanism to determine if the adiabatic following dynamics is trivial or piecewise. This work thus considerably extends our early study on the same topic [Gong and Wang, Phys. Rev. A 97, 052126 (2018)] and shall motivate more interests in non-Hermitian systems.
Exactly solvable piecewise analytic double well potential $V_{D}(x)=min[(x+d)^2,(x-d)^2]$ and its dual single well potential $V_{S}(x)=max[(x+d)^2,(x-d)^2]$
A geometrical approach to non-adiabatic transitions in quantum theory: applications to NMR, over-barrier reflection and parametric excitation of quantum oscillator
本文证明，作为幺正量子演化的结果，一个适当定义的量子熵算符（与非演化的冯诺伊曼熵相反）的期望值只能在非绝热变换中增加，而在绝热变换中保持不变。因此，第二定律的克劳修斯公式被建立为量子力学中的一个定理，在某种程度上，它等价于先前根据最小功原理建立的公式[A. E. Allahverdyan和T. M. Nieuwenhuizen，Phys.Rev.E71，046107（2005）]。然后用一个完全可解的例子，即受迫谐振子，说明了相应的量子力学熵增加原理。注意微正则和正则初始条件。结果进行了比较，他们的经典同行。
