Bistable generalised Langevin dynamics driven by correlated noise possessing a long jump distribution: barrier crossing and stochastic resonance

TL;DR

This paper investigates the dynamics of a generalized Langevin equation with correlated noise exhibiting long jumps, analyzing barrier crossing times and stochastic resonance phenomena in systems with power-law tails.

Contribution

It introduces a model with multiplicative long-jump noise in the generalized Langevin equation, exploring its effects on probability distributions and stochastic resonance behavior.

Findings

Probability densities develop power-law tails over time.

Mean first passage time depends on model parameters.

Stochastic resonance peaks are influenced by memory and passage time.

Abstract

The generalised Langevin equation with a retarded friction and a double-well potential is solved. The random force is modelled by a multiplicative noise with long jumps. Probability density distributions converge with time to a distribution similar to a Gaussian but tails have a power-law form. Dependence of the mean first passage time on model parameters is discussed. Properties of the stochastic resonance, emerging as a peak in the plot of the spectral amplification against the temperature, are discussed for various sets of the model parameters. The amplification rises with the memory and is largest for the cases corresponding to the large passage time.