Unified analysis of terminal-time control in classical and quantum systems

Many phenomena in physics, chemistry, and biology involve seeking an optimal control to maximize an objective for a classical or quantum system which is open and interacting with its environment. The complexity of finding an optimal control for maximizing an objective is strongly affected by the possible existence of sub-optimal maxima. Within a unified framework under specified conditions, control objectives for maximizing at a terminal time physical observables of open classical and quantum systems are shown to be inherently free of sub-optimal maxima. This attractive feature is of central importance for enabling the discovery of controls in a seamless fashion in a wide range of phenomena transcending the quantum and classical regimes.Comment: 10 page

Extracting molecular Hamiltonian structure from time-dependent fluorescence intensity data

We propose a formalism for extracting molecular Hamiltonian structure from inversion of time-dependent fluorescence intensity data. The proposed method requires a minimum of \emph{a priori} knowledge about the system and allows for extracting a complete set of information about the Hamiltonian for a pair of molecular electronic surfaces.Comment: 7pages, no figures, LaTeX2

Optimal use of time dependent probability density data to extract potential energy surfaces

A novel algorithm was recently presented to utilize emerging time dependent probability density data to extract molecular potential energy surfaces. This paper builds on the previous work and seeks to enhance the capabilities of the extraction algorithm: An improved method of removing the generally ill-posed nature of the inverse problem is introduced via an extended Tikhonov regularization and methods for choosing the optimal regularization parameters are discussed. Several ways to incorporate multiple data sets are investigated, including the means to optimally combine data from many experiments exploring different portions of the potential. Results are presented on the stability of the inversion procedure, including the optimal combination scheme, under the influence of data noise. The method is applied to the simulated inversion of a double well system.Comment: 34 pages, 5 figures, LaTeX with REVTeX and Graphicx-Package; submitted to PhysRevA; several descriptions and explanations extended in Sec. I