Mean first-passage time for an overdamped particle in a disordered force field

Area of Science:

• Statistical physics
• Condensed matter physics

Background:

• Understanding particle dynamics in disordered environments is crucial.
• Quenched disorder introduces randomness that significantly impacts particle motion.

Purpose of the Study:

• To derive a rigorous expression for the mean first-passage time (MFPT) of an overdamped particle.
• To investigate the depinning transition in systems with quenched disorder and constant bias.

Main Methods:

• Derivation of a general expression for MFPT.
• Analysis of disorder-averaged MFPT under varying bias.
• Exact calculation of depinning thresholds for specific disorder types.

Main Results:

• A transition from infinite to finite MFPT occurs at a critical bias, signifying a depinning transition.
• Exact depinning thresholds are obtained for Gaussian and generalized kangaroo disorder.
• The effect of force field correlations on particle motion is analyzed for Gaussian disorder.

Conclusions:

• The study provides a theoretical framework for understanding depinning transitions in disordered systems.
• The findings are applicable to various types of quenched disorder, including Gaussian and kangaroo disorder.