  We study the isothermal Brownian dynamics of a particle in a system with
spatially varying diffusivity. Due to the heterogeneity of the system, the
particle's mean displacement does not vanish even if it does not experience any
physical force. This phenomenon has been termed "noise-induced drift", and has
been extensively studied for one-dimensional systems. Here, we examine the
noise-induced drift in a two-dimensional anisotropic system, characterized by a
symmetric diffusion tensor with unequal diagonal elements. A general expression
for the mean displacement vector is derived and presented as a sum of two
vectors, depicting two distinct drifting effects. The first vector describes
the tendency of the particle to drift toward the high diffusvity side in each
orthogonal principal diffusion direction. This is a generalization of the
well-known expression for the noise-induced drift in one-dimensional systems.
The second vector represents a novel drifting effect, not found in
one-dimensional system, originating from the spatial rotation in the directions
of the principal axes. The validity of the derived expressions is verified by
using Langevin dynamics simulations. As a specific example, we consider the
relative diffusion of two transmembrane proteins, and demonstrate that the
average distance between them increases at a surprisingly fast rate of several
tens of micrometers per second.
