论文标题
抛物线和超级抛物线$ \ Mathcal {pt} $中的非绝热过渡
Non-adiabatic transitions in parabolic and super-parabolic $\mathcal{PT}$-symmetric non-Hermitian systems
论文作者
论文摘要
特殊的点，复杂参数空间中的光谱退化点是非热量子系统的基础。在存在特殊点的情况下，非热系统的动力学与赫尔米尔人的动力学有很大不同。在这里，我们研究了非热的$ \ MATHCAL {P} \ MATHCAL {T} $ - 对称系统中的非绝热过渡，其中，在有限的速度或时间函数的有限速度下，特殊点通过时间的时间驱动。我们识别不同的传输动力学，这些动力学以特殊点为单位，并为非绝热传播概率提供了分析近似公式。我们讨论了可能使用$ \ MATHCAL {P} \ MATHCAL {T} $ - 对称的非及格一维紧密的光学波导晶格的实验实现。
Exceptional points, the spectral degeneracy points in the complex parameter space, are fundamental to non-Hermitian quantum systems. The dynamics of non-Hermitian systems in the presence of exceptional points differ significantly from those of Hermitian ones. Here we investigate non-adiabatic transitions in non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric systems, in which the exceptional points are driven through at finite speed which are quadratic or cubic functions of time. We identity different transmission dynamics separated by exceptional points, and derive analytical approximate formulas for the non-adiabatic transmission probabilities. We discuss possible experimental realizations with a $\mathcal{P}\mathcal{T}$-symmetric non-Hermitian one-dimensional tight-binding optical waveguide lattice.
