Exact Current Fluctuations in a Tight-Binding Chain with Dephasing Noise

For a tight-binding chain with dephasing noise on an infinite interval, we exactly calculate the variance of the integrated current for a step initial condition with average densities, $\rho_a$ on the negative axis and $\rho_b$ on the positive axis. Our exact solution reveals that the presence of dephasing, no matter how small, alters the nature of current fluctuations from ballistic to diffusive in the long-time limit. The derivation relies on the Bethe ansatz on the infinite interval and a nontrivial parameter dependence, referred to as the $\omega$-dependence, of the moment generating function for the integrated current. Furthermore, we demonstrate that the asymptotic form of the variance and a numerically obtained cumulant generating function coincide with those in the symmetric simple exclusion process.