Abstract
The dynamics of the density matrix of the two-state system under the influence of time-dependent deterministic and fluctuating forces is investigated. The exact formal solutions for the diagonal and off-diagonal elements are derived and transformed into coupled nonconvolutive master equations and integral relations. Thereby, the evolution of any observable relevant to the two-state system may be described. Solutions of the dynamical equations in analytic form are presented both for high and low temperatures. An iterative numerical method is put forward in which the familiar noninteracting-blip approximation is systematically improved by taking into account all bath-induced nearest-neighbor interblip correlations. The expanded treatment is found to be indispensable in studies of the dynamics of the off-diagonal elements at low temperatures. Finally, we discuss selection rules, as well as possibilities of control of tunneling, which occur in the presence of monochromatic driving.
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