Control of Chaotic Dynamics

Considering the sensitivity of classical chaotic systems to external perturbations, and the ubiquitous nature of chaotic dynamics in larger systems, it is important to 1 establish that quantum mechanics allows for control in chaotic systems as well. [ One simple molecular system that displays quantirm chaos is the rotational exci- tation of a diatomic molecule using pulsed microwave radiation [227], Under the conditions adopted below, this system is a molecular analog of the delta-lacked ij rotor, that is, a rotor that is periodically lacked by a delta fiinction potential, which 4 is a paradigm for chaotic dynamics [228, 229], The observed energy absorption of such systems is called quantum chaotic diffusion. 

If die orientation of a diatomic molecule is described by two angles 9 and (j [230], then the corresponding Hamiltonian is  

Here d is the molecular electric dipole moment, E0 is the amplitude of the drivitt field whose polarization direction defines the z direction, / is the moment of inertiai j of the molecule about an axis perpendicular to the symmetry axis, and A(t/T — ) i the pulse shape function of the form 

Eigenstates of the Hamiltonian H are tij, ntj), where n, is the angular momentum quantum number with projection mj along the z axis. 

As shown by Bliimel and co-workers [227], the Icicked Csl molecule is particularly appropriate candidate for this study since it has a large dipole moment, which increases the molecule-field coupling strength, and the rotation-vibration coupling is small at low excitation energies so that one may consider solely rotational excitation. We consider then the dynamics of Csl in the indicated pulsed field, in a parameter range known to display classical chaos [231]..  

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To demonstrate control of chaotic dynamics, we assume that an initial superposition of Hamiltonian eigenstates of the form [231]... 

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