Stochastic resets in the context of a tight-binding chain driven by an oscillating field

Abstract

In this work, we study in the framework of the so-called driven tight-binding chain (TBC) the issue of quantum unitary dynamics interspersed at random times with stochastic resets mimicking non-unitary evolution due to interactions with the external environment, The driven TBC involves a quantum particle hopping between the nearest-neighbour sites of a one-dimensional lattice and subject to an external forcing field that is periodic in time. We consider the resets to be taking place at exponentially-distributed random times. Using the method of stochastic Liouville equation, we derive exact results for the probability at a given time for the particle to be found on different sites and averaged with respect to different realizations of the dynamics. We establish the remarkable effect of localization of the TBC particle on the sites of the underlying lattice at long times. The system in the absence of stochastic resets exhibits delocalization of the particle, whereby the particle does not have a time-independent probability distribution of being found on different sites even at long times, and, consequently, the mean-squared displacement of the particle about its initial location has an unbounded growth in time. One may induce localization in the bare model only through tuning the ratio of the strength to the frequency of the field to have a special value, namely, equal to one of the zeros of the zeroth order Bessel function of the first kind. We show here that localization may be induced by a far simpler procedure of subjecting the system to stochastic resets.