Relaxation dynamics of a particle in the presence of an external potential: exact solution in terms of matrix continued fractions

W.T. Coffey, Yu.P. Kalmykov and J.T. Waldron

Physica A: Statistical Mechanics and its Applications, 1994, vol. 208, issue 3, 462-478

Abstract: Exact expressions for the Laplace transform of the after effect function arising from the solution of the Langevin or underlying Fokker-Planck equation for Brownian motion in an external potential are obtained as a sum of products of infinite matrix continued fractions. This is accomplished by reducing the scalar multiterm recurrence relations associated with the Fokker-Planck equation to matrix three term recurrence relations. The solution is illustrated by considering the problem of dielectric relaxation of a single axis rotator subjected to both constant and crystalline anisotropy fields.

Date: 1994
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:208:y:1994:i:3:p:462-478

DOI: 10.1016/0378-4371(94)00048-4

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