Variational approach to the diffusion on inhomogeneous lattices

General formulation of the variational approach to the collective diffusion process is presented. The method has been primarily invented to deal with problems of many interacting particles at the homogeneous surfaces. It turned out that the approach can be easily generalized to the cases where diffusion occurs at inhomogeneous lattices. It can be applied to describe interacting and noninteracting adatoms. Diffusion of single particle over lattices of various geometry can be also analyzed within this approach. The use of the method in its general formulation is illustrated in the examples of 1D lattices with random transition rates. Simple results of independent particles in the random lattices can be easily reproduced on using variational approach and solutions for more complicated cases including particle-particle correlation can be derived. It is shown that due to the dynamical correlations increase of the diffusion coefficient can be suppressed or generated depending on the concrete system realizations.