Problems of coherent description of electron transfer reactions

Possible modifications of the Zusman stochastic equations aimed to account for quantum interference of basis states of the system have been investigated. Starting with Caldeira-Leggett theory, we have obtained a set of equations for the density matrix in the Wigner representation that includes nonequilibrium distribution in the momentum space at short time scale. A variant of reduction of the density matrix equation to the Lindblad form has been examined. Modified Zusman equations have been obtained in a strong friction limit. On a simple example the applicability and restrictions of the considered models have been explored and the exact analytical expressions have been obtained. The influence of the initial conditions on a rigidity of the obtained inequalities has been inspected. It has been shown that the applicability of the proposed models is broader compare to the original Zusman equations. At the same time neither of modifications leads to the complete solution of the problem since there is the region of the parameters where the Von Neumann inequalities are broken