Constrained Adiabatic Trajectory Method

The nonadiabatic temporal evolution which is associated with inelastic collisions and photoreactive processes typically produces a final state distribution that differs markedly from the initial state distribution. Nevertheless an adiabatic formalism is often used in a zeroth-order description of the processes; for time-periodic perturbations the Floquet theory has been used within an adiabatic framework to provide a compact dynamical theory which requires a basis composed of only a small number of Floquet eigenstates. The use of the generalized Floquet theory or of the concept of a super-adiabatic basis allows the adiabatic approach to be further extended to handle systems with quasi-periodic Hamiltonians. The present work proposes a new approach, in which the time duration of the interaction is artificially prolonged and special absorbing boundary conditions are introduced asymptotically over the lengthened time interval in such a way as to force the adiabaticity of the process. The method involves what can be thought of as time-dependent optical potentials. Some trial applications to semiclassical inelastic collisions and to photodissociation effects have shown that the use of the new technique permits a description of the dynamical processes which is so economical that the use of a single generalized Floquet eigenvector will suffice. The main technical feature of this constrained adiabatic trajectory method is that it converts the problem of solving the TDSE with an explicitly time-dependent potential into that of solving a static complex eigenvalue problem.