Markovian and non-Markovian solution of the generalized master equation for dynamics of particle transfer in a symmetric double-well potential

Dynamics of particle transfer in a symmetric double-well potential has been investigated. In restriction to two-level system, the convolution form of generalized master equation with retention of off-diagonal matrix elements has been solved on non-Markovian level as well in Markov approximation. It has been shown that subsystem dynamics crucially depends on interplay of three variables, correlation time of an environment, dephasing time and coherent transfer time. The character of dynamics then varies from damped oscillations through exponential decay and incoherent relaxation. It has been shown that on non-Markovian level, under some circumstances, the particle transfer is governed by the dynamics of slow environment.