A new expansion for treating diffusive transport on bond disordered lattices is presented and applied to the bond percolation problem in 3 dimensions. Our approach, when combined with standard resummation techniques, leads to a prediction for the 3-dimensional transport threshold pc = 0.252, which is in excellent agreement with known results. This agreement is obtained without recourse to renormalization group techniques or self-consistent arguments. It originates from a new t-matrix representation for the frequency-dependent diffusion coefficient and is a direct consequence of the equations of motion for the probability currents.
|Original language||English (US)|
|Number of pages||9|
|Journal||Physica A: Statistical Mechanics and its Applications|
|State||Published - Jul 1988|
ASJC Scopus subject areas
- Statistics and Probability
- Condensed Matter Physics