Alberto Castro edited Optimal control.tex  over 9 years ago

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Also, the usual formulation of QOCT assumes the linearity of quantum mechanics. However, the time-dependent Kohn-Sham equations are not linear, and this fact complicates both the theory and the numerics. We therefore extended the basic theory to handle the TDDFT equations, and implemented the resulting equations~\cite{Castro2012a}.  Finally, we enumerate We finish this section citing  some of the applications of the QOCT machinery included in octopus, that can give an idea of the available options: range of possibilities that can be attempted:  \begin{enumerate} 

\item Ref.~\cite{Rasanen2008} studies double quantum dots, and shows how the electron state of these systems can be manipulated with the help of electric fields tailored by QOCT.  \item Ref~\cite{Castro2009e} shows how the shape of femtosecond laser pulses can be tailored in order to obtain maximal ionization of atoms and molecules. The system chosen to demonstrate this possibility is the H$_2^+$ molecule, irradiated with short ($\approx 5$~fs) high intensity laser pulses.  \item Ref~\cite{Kammerlander2011a} inquires about the possibility of using the electronic current to define the target functional of the QOCT formalism.  \item f~\cite{Krieger2011}  \item g~\cite{Castro14}  \item h~\cite{Castro2014} Finally, a series of works have studied the possibility of using optimal control for photo-chemical control: the tailoring of laser pulses to create or break selected bonds in molecules. The underlying physical model should be based on TDDFT, and on a mixed quantum classical scheme (within octopus, Ehrenfest molecular dynamics). Some first attempts in this area were reported in Refs~\cite{Krieger2011,Castro14}. However these works did not consider a fully consistent optimal control theory encompassing TDDFT and Ehrenfest dynamics. This theory has been recently presented~\cite{Castro2014}, and the first computations demonstrating its feasibility will be reported soon.  \end{enumerate}