Vakulchyk I, Fistul M V, Zolotaryuk Y, Flach S
Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon 34051, South Korea.
Chaos. 2018 Dec;28(12):123104. doi: 10.1063/1.5060654.
Discrete time quantum walks are unitary maps defined on the Hilbert space of coupled two-level systems. We study the dynamics of excitations in a nonlinear discrete time quantum walk, whose fine-tuned linear counterpart has a flat band structure. The linear counterpart is, therefore, lacking transport, with exact solutions being compactly localized. A solitary entity of the nonlinear walk moving at velocity would, therefore, not suffer from resonances with small amplitude plane waves with identical phase velocity, due to the absence of the latter. That solitary excitation would also have to be localized stronger than exponential, due to the absence of a linear dispersion. We report on the existence of a set of stationary and moving breathers with almost compact superexponential spatial tails. At the limit of the largest velocity , the moving breather turns into a completely compact bullet.
离散时间量子行走是定义在耦合二能级系统的希尔伯特空间上的酉映射。我们研究非线性离散时间量子行走中激发的动力学，其经过微调的线性对应物具有平带结构。因此，线性对应物缺乏输运，其精确解是紧密局域化的。由于不存在具有相同相速度的小振幅平面波，以速度 移动的非线性行走的单个实体不会与这些平面波发生共振。由于不存在线性色散，该单个激发也必须比指数形式更强地局域化。我们报告了一组具有几乎紧密的超指数空间尾部的驻波和移动呼吸子的存在。在最大速度 的极限情况下，移动呼吸子变成一个完全紧密的子弹态。
