Abstract
We study the diffusion of a Brownian particle quadratically coupled to a
thermally fluctuating field. In the weak-coupling limit, a path-integral
formulation allows us to compute the effective diffusion coefficient in
the cases of an active particle, which tends to suppress field
fluctuations, and of a passive particle, which only undergoes field
fluctuations. We show that the behavior is similar to what was
previously found for a linear coupling: an active particle is always
slowed down, whereas a passive particle is slowed down in a slow field
and accelerated in a fast field. Numerical simulations show a good
agreement with the analytical calculations. The examples of a membrane
protein coupled to the curvature or composition of the membrane are
discussed, with a focus on the room for anomalous diffusion.
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