Stochastic resonance and symmetry breaking in a one-dimensional system

We derive and discuss properties of an exact solution for the average time for trapping of a Brownian particle driven by a random, asymmetric but unbiased, telegraph signal. The particle moves along a line segment terminated by either two traps or a trap and a reflecting point. Numerical results suggest that stochastic resonance, defined as a nonmonotonic behavior of the mean trapping time, is absent in the first case but present in the second. This generalizes a result obtained earlier by Doering and Gadoua [Phys. Rev. Lett. 69, 2318 (1992)] and implies that symmetry breaking alone does not necessarily create stochastic resonance.