Boundary-induced drift and negative mobility in constrained stochastic systems

Area of Science:

• Statistical Physics
• Soft Matter Physics
• Nonlinear Dynamics

Background:

• Stochastic dynamics are fundamental to many physical and biological systems.
• Anisotropic diffusion and boundary interactions are crucial for understanding particle behavior.
• Previous studies often simplified boundary conditions or diffusion properties.

Purpose of the Study:

• To investigate how boundary geometry and anisotropic diffusion generate directed motion.
• To analyze the mechanism of boundary-induced drift in overdamped systems.
• To demonstrate macroscopic transport from local drift using a model system.

Main Methods:

• Analysis of overdamped stochastic dynamics with hard reflecting boundaries.
• Derivation of the local velocity form v_{B}(x)=t(x)^{⊤}Dn(x).
• Modeling with a one-dimensional dimer of particles with unequal diffusion coefficients.

Main Results:

• The combination of boundary geometry and anisotropic diffusion generically produces directed motion.
• No-flux boundary conditions lead to oblique reflections and systematic parallel drift.
• Local boundary-induced drift can accumulate into macroscopic transport.
• Demonstrated sustained center-of-mass motion and absolute negative mobility in a dimer model.

Conclusions:

• Boundary-induced drift is a general mechanism for generating directed motion in confined stochastic systems.
• The interplay between diffusion anisotropy and boundary geometry is key to emergent transport.
• This framework provides insights into active matter and transport phenomena in complex environments.