OPTIMAL-CONTROL OF CLASSICAL MOLECULAR-DYNAMICS - A PERTURBATION FORMULATION AND THE EXISTENCE OF MULTIPLE SOLUTIONS

This paper considers the prospect for there being multiple solutions t o the control of classically modelled molecular dynamical systems. The research presented here follows up on a parallel study based on quant um mechanics. For polyatomic molecules it is generally expected that a classical mechanical model will be adequate and necessary as a means for designing optical fields for molecular control. The prospect for m ultiple control field solutions existing in this domain is important t o establish in terms of ultimate laboratory realization of molecular c ontrol. A general formulation of the multiplicity problem is considere d and the existence df a denumerably infinite number of solutions for the control field amplitude is shown to be the case under certain mild limitations on the physical variables.