Dynamic of the system in a periodic potential, submitted to an electromagnetic wave: Path integral approach

We introduced the formalism of path integrals to describe the dynamics of a system consisting of two particles. One is located in a periodic potential well (first subsystem), while the other particle is outside the well and subjected to a circular electromagnetic field (second subsystem). Thanks to this formalism, we are able to describe the dynamics of our system by a propagator which is the product of two subsystems of propagators. The propagator of the first subsystem is put in the standard form exp[Action] as a result of the coherent spin states. This form of propagator is possible by replacing the spin with a unit vector aligned along the polar and azimuthal directions. The second subsystem propagator come with the use of the Feynman-Vernon functional on the subsystem. Thanks to its two propagators, we have succeeded in explicitly and analytically evaluating the dynamics of our dissipative quantum system by a single propagator. Using this fundamental result, we evaluated the special case where the second subsystem bathed in a super-ohmic environment. (paper)