Modeling Escape from a One-Dimensional Potential Well at Zero or Very Low Temperatures

TL;DR

This paper systematically investigates the escape process from a one-dimensional potential well at very low temperatures, revealing deviations from classical models due to initial conditions and intrinsic oscillations.

Contribution

It introduces a detailed analysis of escape dynamics at low temperatures, highlighting the limitations of the standard Kramers model under certain conditions.

Findings

Deviations from Kramers model occur at low temperatures and dissipation.

Initial conditions significantly influence escape responses.

Intrinsic oscillations affect activation processes at T=0.

Abstract

The process of activation out a one-dimensional potential is investigated systematically in zero and nonzero temperature conditions. The features of the potential are traced through statistical escape out of its wells whose depths are tuned in time by a forcing term. The process is carried out on the damped pendulum system imposing specific initial conditions on the potential variable. While for relatively high values of the dissipation the statistical properties follow a behavior that can be derived from the standard Kramers model, decreasing the dissipation we observe responses/deviations which 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.