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In this work, we study in the framework of the so-called driven tight-bindingchain (TBC) the issue of quantum unitary dynamics interspersed at random timeswith stochastic resets mimicking non-unitary evolution due to interactions withthe external environment, The driven TBC involves a quantum particle hoppingbetween the nearest-neighbour sites of a one-dimensional lattice and subject toan external forcing field that is periodic in time. We consider the resets tobe taking place at exponentially-distributed random times. Using the method ofstochastic Liouville equation, we derive exact results for the probability at agiven time for the particle to be found on different sites and averaged withrespect to different realizations of the dynamics. We establish the remarkableeffect of localization of the TBC particle on the sites of the underlyinglattice at long times. The system in the absence of stochastic resets exhibitsdelocalization of the particle, whereby the particle does not have atime-independent probability distribution of being found on different siteseven at long times, and, consequently, the mean-squared displacement of theparticle about its initial location has an unbounded growth in time. One mayinduce localization in the bare model only through tuning the ratio of thestrength to the frequency of the field to have a special value, namely, equalto one of the zeros of the zeroth order Bessel function of the first kind. Weshow here that localization may be induced by a far simpler procedure ofsubjecting the system to stochastic resets.

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