Underdamped, anomalous kinetics in double-well potentials

TL;DR

This paper investigates how underdamped dynamics in a double-well potential differ from overdamped cases, revealing that transition rate ratios depend on both barrier widths and heights under full dynamics, supported by analytical and numerical evidence.

Contribution

It provides the first analytical and numerical comparison of transition rates in underdamped versus overdamped regimes with non-equilibrium noise.

Findings

Transition rate ratios depend on barrier widths and heights in underdamped dynamics.

Overdamped case transition ratios depend only on barrier width.

Analytical formulas are validated by extensive numerical simulations.

Abstract

The noise driven motion in a bistable potential acts as the archetypal model of various physical phenomena. Here, we contrast the overdamped dynamics with the full (underdamped) dynamics. For the overdamped particle driven by a non-equilibrium, $\alpha$-stable noise the ratio of forward and backward transition rates depends only on the width of a potential barrier separating both minima. Using analytical and numerical methods, we show that in the regime of full dynamics, contrary to the overdamped case, the ratio of transition rates depends both on widths and heights of the potential barrier. The analytical formula for the ratio of transition rates is corroborated by extensive numerical simulations.