Effective decoherence of realistic clocks: General theory and application to a topological insulator

Abstract

It has been well established that the evolution of an isolated quantum system can appear as undergoing pure dephasing to an observer using an imperfect clock. In this work, we apply this theory to the transport phenomenon in open quantum systems. Starting with a system intrinsically undergoing nonunitary evolution in ideal time, we consider the effect of a realistic clock that approaches Gaussian distribution in the long-time limit. For quantum transport, it eventually leads to a general physical prediction: a stable probability current in a quantum transport system must be robust against any transformation that conforms with a simple formula given by an ideal Gaussian stationary clock. This understanding of quantum transport is demonstrated numerically in a topological insulator, where it also explains the robustness of the quantum Hall response against pure dephasing.