Dynamical stable-jump–stable-jump picture in a non-periodically driven quantum relativistic kicked rotor system**Project supported by the National Natural Science Foundation of China (Grant Nos. 11535004, 11761161001, 11375086, 11120101005, 11175085, and 1235001), the National Major State Basic Research and Development Program of China (Grant No. 2016YFE0129300), and the Science and Technology Development Fund of Macau (Grant No. 068/2011/A).

Abstract

We study a non-periodically driven kicked rotor based on the one-dimensional quantum relativistic kicked rotor (QRKR). In our model, we add a small constant to the interval of the one-dimensional QRKR after each kick process. It is found that the momentum spreading is stable in finite kicked times, it then jumps up or down and becomes stable again. This interesting phenomenon is understood by quantum resonance. Moreover, the stable-jump–stable-jump phenomenon persists, even though the interval of kick process is randomly increased. This result means that the quantum resonance is independent of the periodic perturbation in the QRKR model.