RELAXATION DYNAMICS OF A PARTICLE IN THE PRESENCE OF AN EXTERNAL POTENTIAL - EXACT SOLUTION IN TERMS OF MATRIX CONTINUED FRACTIONS

Exact expressions for the Laplace transform of the after effect functi on arising from the solution of the Langevin or underlying Fokker-Plan ck equation for Brownian motion in an external potential are obtained as a sum of products of infinite matrix continued fractions. This is a ccomplished by reducing, the scalar multiterm recurrence relations ass ociated with the Fokker-Planck equation to matrix three term recurrenc e relations. The solution is illustrated by considering the problem of dielectric relaxation of a single axis rotator subjected to both cons tant and crystalline anisotropy fields.