Upper and lower bounds on the control field and the quality of achieved optimally controlled quantum molecular motion

Metin Demiralp, Herschel Albert Rabitz

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

A large class of problems in optimally controlled quantum or classical molecular dynamics has multiple solutions for the control field amplitude. A denumerably infinite number of solutions may exist depending on the structure of the design cost functional. This fact has been recently proved with the aid of perturbation theory by considering the electric field as the perturbating agent. In carrying out this analysis, an eigenvalue (i.e., a spectral parameter) appears which gives the degree of deviation of the control objective from its desired value. In this work, we develop a scheme to construct upper and lower bounds for the field amplitude and spectral parameter for each member of the denumerably infinite set of control solutions. The bounds can be tightened if desired. The analysis here is primarily restricted to the weak field regime, although the bounds for the strong field nonlinear case are also presented.

Original languageEnglish (US)
Pages (from-to)337-352
Number of pages16
JournalJournal of Mathematical Chemistry
Volume19
Issue number3
DOIs
StatePublished - Jan 1 1996

All Science Journal Classification (ASJC) codes

  • Chemistry(all)
  • Applied Mathematics

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