Exact computation of the mobility of a diffusing particle in a defective lattice gas under an external field

We give a method for the exact computation of the mobility of a particle diffusing in a lattice gas with defects. We describe the method by considering its application to the computation of the mobility of a particle diffusing in a lattice with defects in the form of dead-ends. The mobility initially increases linearly with field intensity, then crosses over to a nonlinear behaviour and reaches a maximum. Beyond this point the mobility decreases with increasing field intensity, showing an anomalous behaviour which may be attributed to partial confinement imposed by the field. The proposed method is general and may be applied to the computation of arbitrary moments of the probability function of a single particle diffusing in a lattice gas with defects of arbitrary characteristics.