Semiclassical optimal control theory

As demonstrated above, bond-selective dissociation can be achieved with high efficiency by using an initial displaced-position and/or a directed-momentum wavepacket. The latter wavepacket can be prepared via the sequence of quadratically chirped pulses or by using semiclassical optimal control theory [34,35],... 

Summary. An efficient semiclassical optimal control theory for controlling wave-packet dynamics on a single adiabatic potential energy surface applicable to systems with many degrees of freedom is discussed in detail. The approach combines the advantages of various formulations of the optimal control theory quantum and classical on the one hand and global and local on the other. The efficiency and reliability of the method are demonstrated, using systems with two and four dimensions as examples. 

Recently, a semiclassical formulation of the optimal control theory has been derived [23, 24] by combining the conjugate gradient search method... 

As this approach deals with a set of classical trajectories, its numerical cost remains reasonable for multidimensional systems. Contrary to the classical approach, which controls only the averaged classical quantities, the present semiclassical method can control the quantum motion itself. This makes it possible to reproduce almost all quantum effects at a computational cost that does not grow too rapidly as the dimensionality of the system increases. The new approach therefore combines the advantages of the quantum and classical formulations of the optimal control theory. 

The approach has been tested by controlling nuclear wavepacket motion in a two-dimensional model system [23], The relative simplicity of the system makes it possible to compare the semiclassical results with exact quantum ones. Numerical applications to the control of HCN-CNH isomerization [24] demonstrates that the new semiclassical formulation of optimal control theory provides an effective and powerful tool for controlling molecular dynamics with many degrees of freedom. 

In order to demonstrate the efficiency and accuracy of the semiclassical formulation of optimal control theory, let us consider the control of two elementary types of motion (a) a shift of the position of the ground-state wavepacket in the two-dimensional model system of H20 and (b) an acceleration of the ground-state wavepacket at the same position in the same model. 

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