Relaxation time for nonlinear response of a Brownian particle subject to a step external force:Analytical solutions for one-dimensional models

The nonlinear response to a step external force of a system with relaxational dynamics governed by a one-dimensional Fokker-Planck equation is considered. An exact analytical expression for the step response nonlinear relaxation time is derived in terms of an integral (which can be evaluated numerically). Applications to nonlinear problems concerning the dynamic Kerr effect, dielectric relaxation of liquid dielectrics, and magnetic relaxation of systems of single domain ferromagnetic particles are given. The results are compared with solutions previously obtained.