Topology of Classical Molecular Optimal Control Landscapes in Phase Space

Details Topology of Classical Molecular Optimal Control Landscapes in Phase Space Topology of Classical Molecular Optimal Control Landscapes in Phase Space

2011-08-18

arxiv.org/abs/1108.3806v1

Physics

Chemical Physics

Scientific paper

Optimal control of molecular dynamics commonly adopts a quantum mechanical perspective. However, the preponderance of molecular dynamics studies for a variety of purposes utilize classical mechanical models. This paper treats laser-driven optimal control of molecular dynamics in a classical framework. We consider the objective of steering the system from an initial point in phase space to a target point, subject to the dynamic constraint of Hamilton's equations. The classical control landscape corresponding to this objective is a functional of the control field, and the topology of the landscape is analyzed through its gradient and Hessian with respect to the control. Under specific assumptions, the classical control landscape is found to be free of traps that could hinder reaching the objective. The Hessian associated with an optimal control field is shown to have finite rank, indicating the presence of an inherent degree of robustness to control noise. Extensive numerical simulations are performed, confirming the absence of traps in the classical control landscape. The specific case of a controlled anharmonic oscillator is presented to illustrate the theoretical principles. A comparison is made between the classical formulation and the mathematically analogous quantum state-to-state transition probability control landscape.

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