Quasipercolation: Charge transport in fluctuating systems

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Abstract
Mobility of charge carriers in certain liquid systems is controlled by temporal fluctuations in local conductivity. Fast transport proceeds along high mobility regions similarly to traditional percolation with the difference that these regions form and fade away with fluctuations. By making use of the idea of waiting time distribution of continuous time random walk, formulas for relative mobility as a function of the expectation value of proportion of high mobility regions are suggested. The results compare reasonably well with experimental data. Under the experimental conditions given quasipercolation theory and the effective medium theory of traditional percolation do not differ too much numerically. For site percolation threshold in nonfluctuating systems the expression [(e−1)/ez]1/2 is suggested, where e is the base of natural logarithm and z is the coordination number.