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We study the effective diffusion constant of a Brownian particle linearlycoupled to a thermally fluctuating scalar field. We use a path integral methodto compute the effective diffusion coefficient perturbatively to lowest orderin the coupling constant. This method can be applied to cases where the fieldis affected by the particle (an active tracer), and cases where the tracer ispassive. Our results are applicable to a wide range of physical problems, froma protein diffusing in a membrane to the dispersion of a passive tracer in arandom potential. In the case of passive diffusion in a scalar field, we showthat the coupling to the field can, in some cases, speed up the diffusioncorresponding to a form of stochastic resonance. Our results on passivediffusion are also confirmed via a perturbative calculation of the probabilitydensity function of the particle in a Fokker-Planck formulation of the problem.Numerical simulations on simplified systems corroborate our results.

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