TY - JOUR

T1 - An analysis and extension of the continuous time random walk method. I. Theory

AU - Halpern, V.

PY - 1981

Y1 - 1981

N2 - The usual continuous time random walk (CTRW) method for analysing the motion of particles between discrete localised states in disordered systems is fairly simple to apply but involves an averaging procedure whose accuracy is unknown. The Laplace transform of the rate equations for such a system is expressed in matrix form, and it is shown that the usual CTRW approximation corresponds to a certain decoupling of their configurational average. This is the first of a hierarchy of CTRW(n) approximations, which treat exactly transitions involving n steps, and conditions are established for the convergence of this series of approximations.

AB - The usual continuous time random walk (CTRW) method for analysing the motion of particles between discrete localised states in disordered systems is fairly simple to apply but involves an averaging procedure whose accuracy is unknown. The Laplace transform of the rate equations for such a system is expressed in matrix form, and it is shown that the usual CTRW approximation corresponds to a certain decoupling of their configurational average. This is the first of a hierarchy of CTRW(n) approximations, which treat exactly transitions involving n steps, and conditions are established for the convergence of this series of approximations.

UR - http://www.scopus.com/inward/record.url?scp=0009310471&partnerID=8YFLogxK

U2 - 10.1088/0022-3719/14/22/014

DO - 10.1088/0022-3719/14/22/014

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AN - SCOPUS:0009310471

SN - 0022-3719

VL - 14

SP - 3195

EP - 3207

JO - Journal of Physics C: Solid State Physics

JF - Journal of Physics C: Solid State Physics

IS - 22

M1 - 014

ER -