First-passage-time statistics for diffusion processes with an external random force

Coherent and incoherent trapping of a diffusion-assisted system in the presence of an external periodic field

Field induced trapping on a line segment of a diffusion-driven system is studied with an aim to gain an insight into the occurrence of coherent stochastic resonance, which is thoroughly explored as synchronized mean-free passages to the traps. Synchronization (coherence) between the external bias, the noise in the system and the temporal trapping events is found to attain an optimum value by increasing the forcing frequency towards the relevant resonant frequency, revealing a minimum in the nonmonotonic mean-free-passage time (MFPT) to trapping. The MFPT at a given forcing frequency, is also nonmonotonic when considered as a function of the diffusion coefficient of the medium, and reveals a maximum exhibiting the least synchronization effect (incoherent trapping).

Symmetry breaking in one-dimensional diffusion

The mean free passage time for one-dimensional diffusion on a line segment under the influence of a deterministic telegraph signal proves to be a nonmonotonic function of the signal rate ("stochastic resonance") if symmetry breaking takes place. The symmetry breaking may be expressed either in nonsymmetric boundary conditions (one end absorbing and the other reflecting) or in a nonsymmetric telegraph signal. The latter case is considered in detail. It turns out that the larger the asymmetry of a telegraph signal, the wider the range of parameters for which a stochastic resonance occurs.

Stochastic resonance in one-dimensional diffusion with one reflecting and one absorbing end point

An analysis of the nonmonotonic dependence of the mean-free-passage time on the frequency of a periodic signal [stochastic resonance (SR)] for diffusion on a segment with one absorbing and one reflecting end point shows that SR exists only for some restricted values of parameters. SR always exists if the periodic telegraph signal is replaced by a random one. The latter case is considered in detail.