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Drifted escape from the finite interval.

Karol Capała1, Bartłomiej Dybiec1

  • 1Institute of Theoretical Physics and Mark Kac Center for Complex Systems Research, Jagiellonian University, Łojasiewicza 11, 30-348 Kraków, Poland.

Physical Review. E
|July 20, 2022
PubMed
Summary

This study investigates noise-driven escape kinetics, showing that mean first passage time reveals universal patterns. This helps distinguish between drift-dominated and random force-dominated systems.

Area of Science:

  • Physics
  • Physical Chemistry
  • Statistical Mechanics

Background:

  • Noise-driven systems exhibit escape kinetics influenced by both stochastic and deterministic forces.
  • Understanding these dynamics is crucial in various scientific fields, including physics and chemistry.

Purpose of the Study:

  • To explore the properties of overdamped drifted escape from finite intervals under symmetric alpha-stable noises.
  • To identify a universal pattern in mean first passage time for discriminating drift- vs. random force-dominated regimes.

Main Methods:

  • Analysis of overdamped Langevin dynamics with symmetric alpha-stable noise.
  • Investigation of mean first passage time under varying generalized Pécklet numbers.

Main Results:

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  • The properly rescaled mean first passage time exhibits a universal pattern as a function of the generalized Pécklet number.
  • This pattern effectively differentiates between drift-dominant and random force-dominant dynamics.
  • Alpha-stable noise can reduce the impact of drift even when drift forces are prevalent.

Conclusions:

  • The generalized Pécklet number serves as a key parameter for characterizing escape dynamics in the presence of drift and alpha-stable noise.
  • The findings provide a method for efficiently distinguishing between different dominance regimes in stochastic systems.
  • Symmetric alpha-stable noises offer unique properties that can modulate the influence of deterministic drift.