Fractionally diffusing passing through the saddle point of metastable potential

TL;DR

This paper investigates how fractional Brownian particles escape over saddle points in metastable potentials, revealing anomalous behaviors related to the fractional exponent that differ from standard Brownian motion.

Contribution

It introduces the study of fractional Brownian motion in metastable potentials, highlighting the impact of the fractional exponent on escape probabilities and dynamics.

Findings

Escape probability is highly dependent on the fractional exponent α.

Particles exhibit reverse property movement when α is large, contrary to normal Brownian motion.

Anomalous diffusion behaviors are observed despite near-zero effective friction.

Abstract

The diffusion of a fractional Brownian particle passing over the saddle point is studied in the field of the metastable potential. The barrier escaping probability is found to be greatly related to the fractional exponent $\alpha$. Properties are revealed to move reversely in the opposite direction of diffusion when $\alpha$ is relatively large despite of the zero-approximating effective friction of the system. This is very anomalous to the standard Brownian motion.