论文标题
自以为是的触发动态过渡
Self-duality triggered dynamical transition
论文作者
论文摘要
关于无旋转量子系统的动力学的一个基本结果是，马里兰州模型在任何维度上都表现出动态定位。在这里，我们实施数学光谱理论和数值实验，以表明当二维马里兰州模型赋予Spin 1/2时，该结果并不成立，此后称为Spin-Maryland（SM）模型。取而代之的是，在一个SM模型家族中，调整（有效的）普朗克常数驱动动态定位{拓扑性质的离域化过渡。这些过渡是由自偶性触发的，自偶和性是由参数中的某些转换产生的对称性 - 逆Planck常数 - 空间。这为新的动态现象提供了重要的见解，例如在跨量子踢转子中发生的情况。
A basic result about the dynamics of spinless quantum systems is that the Maryland model exhibits dynamical localization in any dimension. Here we implement mathematical spectral theory and numerical experiments to show that this result does not hold, when the 2-dimensional Maryland model is endowed with spin 1/2 -- hereafter dubbed spin-Maryland (SM) model. Instead, in a family of SM models, tuning the (effective) Planck constant drives dynamical localization{delocalization transitions of topological nature. These transitions are triggered by the self-duality, a symmetry generated by some transformation in the parameter -- the inverse Planck constant -- space. This provides significant insights to new dynamical phenomena such as what occur in the spinful quantum kicked rotor.
