Electric-circuit simulation of the Schr\"odinger equation and non-Hermitian quantum walks
Abstract
Recent progress has witnessed that various topological physics can be simulated by electric circuits under alternating current. However, it is still a nontrivial problem if it is possible to simulate the dynamics subject to the Schr\"odinger equation based on electric circuits. In this work, we reformulate the Kirchhoff law in one dimension in the form of the Schr\"odinger equation. As a typical example, we investigate quantum walks in LC circuits. We also investigate how quantum walks are different in topological and trivial phases by simulating the Su-Schrieffer-Heeger model in electric circuits. We then generalize them to include dissipation and nonreciprocity by introducing resistors, which produce non-Hermitian effects. We point out that the time evolution of one-dimensional quantum walks is exactly solvable with the use of the generating function made of the Bessel functions.