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 Schrödinger 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.
B. D. Bookout and P. E. Parris, "Long-Range Random Walks on Energetically Disordered Lattices," Physical Review Letters, vol. 71, no. 1, pp. 16 - 19, American Physical Society (APS), Jul 1993.
The definitive version is available at https://doi.org/10.1103/PhysRevLett.71.16
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© 1993 American Physical Society (APS), All rights reserved.
01 Jul 1993