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

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

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.

Suggested Citation

  • Coffey, W.T. & Kalmykov, Yu.P. & Waldron, J.T., 1994. "Relaxation dynamics of a particle in the presence of an external potential: exact solution in terms of matrix continued fractions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 208(3), pages 462-478.
    • Handle: RePEc:eee:phsmap:v:208:y:1994:i:3:p:462-478
    DOI: 10.1016/0378-4371(94)00048-4
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    1. Coffey, Joseph D., 0. "Rural Development Policy And Balanced National Growth," Increasing Understanding of Public Problems and Policies, Farm Foundation.
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