Slow oscillating dynamics of a two-level system subject to a fast telegraph noise: beyond the NIBA approximation

We study the dynamics of a two-site model in which the tunneling amplitude between the sites is not constant but rather a high-frequency noise. Obviously, the population imbalance in this model decays exponentially with time. Remarkably, the decay is modified dramatically when the level asymmetry fluctuates in-phase with fluctuations of the tunneling amplitude. For particular type of these in-phase fluctuations, namely, the telegraph noise, we find the exact solution for the average population dynamics. It appears that the population imbalance between the sites starting from 1 at time $t=0$ approaches a constant value in the limit $t\rightarrow \infty$. At finite bias, the imbalance goes to zero at $t\rightarrow \infty$, while the dynamics of the decay governed by noise acquires an oscillatory character.