A perturbative path integral study of active and passive tracer diffusion in fluctuating fields

Abstract

We study the effective diffusion constant of a Brownian particle linearly coupled to a thermally fluctuating scalar field. We use a path integral method to compute the effective diffusion coefficient perturbatively to lowest order in the coupling constant. This method can be applied to cases where the field is affected by the particle (an active tracer), and cases where the tracer is passive. Our results are applicable to a wide range of physical problems, from a protein diffusing in a membrane to the dispersion of a passive tracer in a random potential. In the case of passive diffusion in a scalar field, we show that the coupling to the field can, in some cases, speed up the diffusion corresponding to a form of stochastic resonance. Our results on passive diffusion are also confirmed via a perturbative calculation of the probability density function of the particle in a Fokker-Planck formulation of the problem. Numerical simulations on simplified systems corroborate our results.

13 pages RevTex, 4 figures

References in corpus (14)

• Sedimentation of active colloidal suspensions
• Symmetries of generating functionals of Langevin processes with colored multiplicative noise
• Corrections to the Saffman-Delbruck mobility for membrane bound proteins
• Lateral diffusion of a protein on a fluctuating membrane
• Hybrid Elastic/Discrete-Particle Approach to Biomembrane Dynamics with Application to the Mobility of Curved Integral Membrane Proteins
• Diffusion on Ruffled Membrane Surfaces
• Drag forces in classical fields
• Diffusing proteins on a fluctuating membrane: Analytical theory and simulations
• Curvature-coupling dependence of membrane protein diffusion coefficients
• Drag forces on inclusions in classical fields with dissipative dynamics
• Effective temperatures of a heated Brownian particle
• Diffusion of active tracers in fluctuating fields
• Dynamical transition for a particle in a squared Gaussian potential
• Self Similar Renormalization Group Applied to Diffusion in non-Gaussian Potentials

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