  In this work, the effect of fluctuations in a disordered square lattice on
diffusion of a test particle is studied using kinetic Monte Carlo simulations.
Diffusion is relevant to a wide variety of problems, both within physics and
outside of physics. Kinetic effects in diffusion are often hidden in a
thermodynamical description of the problem. In this work, no assumptions based
on energy are made, and diffusion occurs purely based on the attempt rate of
the test particle and the occupation and fluctuation rate of the lattice.
Although the average transition rate of the particle is the same for a static
or fluctuating lattice with specific occupation, the diffusion constant is
kinetically affected in a fluctuating, disordered lattice. If the lattice
fluctuates faster than the attempt rate of the particle, diffusion is
controlled by the attempt rate of the particle. However, if the lattice
fluctuates slower than the attempt rate of the particle, diffusion is affected
by the fluctuations. The slower the lattice fluctuates, the lower the diffusion
constant. Furthermore, it is found that for fast fluctuating lattices,
diffusion is due to Brownian motion. If the lattice fluctuates slower than the
particle, diffusion becomes anomalous depending on the occupation of the
lattice.
