标题： 量子随机行走与引力波 显示英文标题

标题： Quantum walks and gravitational waves

摘要： 引入了一类在规则的$(1+2)$D 时空晶格上传播的离散时间量子行走（DTQWs）的新族。这些 DTQWs 的连续极限被证明与狄拉克费米子与任意相对论引力场相互作用的动力学一致。该族被用于建模任意线性引力波（GWs）对 DTQWs 的影响。详细研究了纯剪切引力波。在大空间尺度上，纯剪切引力波不会改变费米子本征模式的极化，但会以一个共同因子重新缩放所有能量。在通常相当于两到三个晶格步长的小尺度上，极化和能量都以非平凡的方式被修改。这种效应在费米子本征模式之间的干涉图样中尤为显著。 显示英文摘要

摘要： A new family of discrete-time quantum walks (DTQWs) propagating on a regular $(1+2)$D spacetime lattice is introduced. The continuous limit of these DTQWs is shown to coincide with the dynamics of a Dirac fermion interacting with an arbitrary relativistic gravitational field. This family is used to model the influence of arbitrary linear gravitational waves (GWs) on DTQWs. Pure shear GWs are studied in detail. On large spatial scales, pure shear GWs do not modify the polarizations of the fermion eigen-modes, but rescale all energies by a common factor. On smaller scales typically comparable to two or three lattice steps, both polarizations and energies are modified in a non-trivial way. This effect is particularly salient on interference patterns between the fermion eigen-modes.