  We investigate the effect of a two-level jump process or random telegraph
noise on a square wave driven tight-binding lattice. In the absence of the
noise, the system is known to exhibit dynamical localization for specific
ratios of the amplitude and the frequency of the drive. We obtain an exact
expression for the probability propagator to study the stability of dynamical
localization against telegraph noise. Our analysis shows that in the presence
of noise, a proper tuning of the noise parameters destroys dynamical
localization of the clean limit in one case, while it induces dynamical
localization in an otherwise delocalized phase of the clean model. Numerical
results help verify the analytical findings. A study of the dynamics of
entanglement entropy from an initially half-filled state offers complementary
perspective.
