Electromagnetic lattice gauge invariance in two-dimensional discrete-time quantum walks
Electromagnetic lattice gauge invariance in two-dimensional discrete-time quantum walks
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DOI：
10.1103/physreva.98.032333
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发表时间：
2018-09-28
影响因子：
2.9
通讯作者：
Perez, Armando
中科院分区：
文献类型：
--
作者：
Marquez-Martin, Ivan;Arnault, Pablo;Perez, Armando
规范不变性是物理学中较为重要的概念之一。我们结合在一维和二维空间中离散时间量子行走的幺正演化来讨论这一概念，此时它们包含与合成的外部电磁场的相互作用。我们引入这种相互作用作为起到规范场作用的附加相位。在此，我们提出一种纳入这些相位的方法，它不同于以往的工作。我们的方案使得在规范变换下出现的离散导数能够以类似于标准格点规范理论的方式，在同等基础上处理时间和空间。通过考虑演化的两步，我们定义了一个规范不变且守恒的密度流。在连续极限下，在对参数进行适当选择的情况下，粒子的动力学变成狄拉克方程，并且守恒流满足相应的守恒方程。
Gauge invariance is one of the more important concepts in physics. We discuss this concept in connection with the unitary evolution of discrete-time quantum walks in one and two spatial dimensions, when they include the interaction with synthetic, external electromagnetic fields. One introduces this interaction as additional phases that play the role of gauge fields. Here, we present a way to incorporate those phases, which differs from previous works. Our proposal allows the discrete derivatives, that appear under a gauge transformation, to treat time and space on the same footing, in a way which is similar to standard lattice gauge theories. By considering two steps of the evolution, we define a density current which is gauge invariant and conserved. In the continuum limit, the dynamics of the particle, under a suitable choice of the parameters, becomes the Dirac equation and the conserved current satisfies the corresponding conservation equation.