Long-range random walks on energetically disordered lattices

Although the master equation describing long-range random walks on an energetically disordered lattice is governed by a nonsymmetric transition matrix W, it may be mapped through a similarity transform onto an imaginary-time Schr\"odinger equation governed by a Hermitian (Hamiltonian) operator H₀ having a nondegenerate ground state. Under this mapping the diffusion constant D can be expressed in terms of the exact ground state energy of operators that are infinitesimally perturbed from H₀.