标题： 非自治厄米或非厄米系统的自发对称性破缺 显示英文标题

标题： Spontaneous symmetry breaking for nonautonomous Hermitian or non-Hermitian systems

摘要： 这里我们首先提出了一种替代方法来解决具有时变厄米算符或伪厄米算符的薛定谔方程，这种方法是对刘易斯和赖森费尔德定理的推广。然后，我们将这个框架应用于与这些哈密顿量相关的时变反线性对称性的自发破缺问题。我们证明，如果一般反线性对称性未被破坏，刘易斯-赖森费尔德相位将是时间的实数奇函数，这使得我们可以恢复时不变伪厄米算符哈密顿量的实谱。对于自发破缺的情况，刘易斯-赖森费尔德相位的虚部会成为时间的偶函数，导致未破缺区域的实特征值发生合并。我们以一个描述非厄米动态Casimir效应的时变哈密顿量为例，展示了未破缺和破缺情况下$\mathcal{PT}$对称性的特性。 显示英文摘要

摘要： Here we first present an alternative approach to the Lewis & Riesenfeld theorem for solving the Schr\"odinger equation for time-dependent Hermitian or pseudo-Hermitian Hamiltonians. Then, we apply this framework to the problem of spontaneous breaking of time-dependent antilinear symmetries associated with those Hamiltonians. We demonstrate that if the general antilinear symmetry is unbroken, the Lewis & Riesenfeld phases are real odd functions of time, which allows up to recover the real spectra of time-independent pseudo-Hermitian Hamiltonians. For the spontaneously broken regime, imaginary components of the Lewis & Riesenfeld phases arise as even functions of time, resulting in the coalescence of the real eigenvalues of the unbroken regime. We present an illustrative example of the unbroken and broken $\mathcal{PT}$-symmetry for a time-dependent Hamiltonian modeling the non-Hermitian dynamical Casimir effect.