Crossover from percolation to diffusion

A problem of the crossover from percolation to diffusion transport is considered. A general scaling theory is proposed. It introduces phenomenologically four critical exponents which are connected by two equations. One exponent is completely new. It describes the increase of the diffusion below percola-tion threshold. As an example, an exact solution of one dimensional lattice problem is given. In this case the new exponent q = 2. Percolation theory is often used to describe transport properties of disordered systems with a large disorder. The typical problems are random mixture of conducting and non-conducting elements, or hopping conduction [1]. The regular percolation theory assumes that the random elements do not change their positions with time so that the percolation paths do not change their spatial locations. The low-temperature electron transport is one of examples where this assumption is not valid. Due to electron-electron interaction the random potential persistently and substantially changes with time [2,3], which may affect conductivity near the metal-insulator transition. Such problems appear outside solid state physics as well. The class of this problem is known as dynamical percolation. They have been studied theoretically using effective medium approximation (See e.g. Ref. [4] and references therein). One dimensional problems of this type have been considered for some models without any approximations [5]. We concentrate here on the case when the diffusion through conducting media is drastically faster then the fluctuations of the positions of the conducting and non-conducting elements. In this case the transition from diffusion to percolation mechanism has all features 1