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Area of Science:

  • Statistical physics
  • Soft matter physics
  • Non-equilibrium systems

Background:

  • Active Brownian particles (ABPs) and run-and-tumble particles (RTPs) are models for self-propelled microscopic objects.
  • Understanding particle escape from confining potentials is crucial in various physical and biological processes.
  • Existing models often focus on equilibrium systems or simplified noise limits.

Purpose of the Study:

  • To investigate the noise-driven escape dynamics of ABPs and RTPs from confining potentials.
  • To derive exact expressions for escape rates in the small noise limit across dimensions.
  • To analyze the influence of potential barrier shape on escape behavior.

Main Methods:

  • Development of a variational approach to calculate escape rates in the small noise limit for arbitrary dimensions.
  • Analytical solution for one-dimensional run-and-tumble particles, including subleading corrections.
  • Two-dimensional analysis of escape from quadratic wells for both ABPs and RTPs.

Main Results:

  • An exact expression for the escape rate was derived using a variational problem in the small noise limit.
  • Explicit solutions and corrections were obtained for one-dimensional RTPs.
  • In 2D, escape rate depends on the full potential barrier shape, not just its height, leading to counterintuitive behaviors like escaping over higher barriers.

Conclusions:

  • The escape dynamics of active particles are significantly influenced by the detailed potential landscape.
  • Unusual phenomena, such as preferential escape over higher barriers and discontinuous switching of escape routes, are observed.
  • These findings reveal a dynamical phase transition dependent on self-propulsion speed, distinct from equilibrium escape.