We investigate the Brownian diffusion of particles in one spatial dimension and in the presence of finite regions within which particles can either evaporate or be reset to a given location. For open boundary conditions, we highlight the appearance of a Brownian yet non-Gaussian diffusion: At long times, the particle distribution is non-Gaussian but its variance grows linearly in time. Moreover, we show that the effective diffusion coefficient of the particles in such systems is bounded from below by 1−2/π times their bare diffusion coefficient. For periodic boundary conditions, i.e., for diffusion on a ring with resetting, we demonstrate a “gauge invariance” of the spatial particle distribution for different choices of the resetting probability currents, in both stationary and nonstationary regimes. Finally, we apply our findings to a stochastic biophysical model for the motion of RNA polymerases during transcriptional pauses, deriving analytically the distribution of the length of cleaved RNA transcripts and the efficiency of RNA cleavage in backtrack recovery.
