Modeling escape from a one-dimensional potential well at zero or very low temperatures

Abstract

The process of activation from a one-dimensional potential is systematically investigated in zero and nonzero temperature conditions. The features of the potential are traced through statistical escape from its wells, whose depths are tuned in time by a forcing term. The process is carried out for the damped pendulum system imposing specific initial conditions on the potential variable. While the escape properties can be derived from the standard Kramers theory for relatively high values of the dissipation, for very low dissipation, these deviate from this theory by being dependent on the details of the initial conditions and the time dependence of the forcing term. The observed deviations have regular dependencies on initial conditions, temperature, and loss parameter itself. It is shown that failures of the thermal activation model are originated at low temperatures and very low dissipation, by the initial conditions and intrinsic, namely, T = 0, characteristic oscillations of the potential-generated dynamical equation.