The calculation of the dynamics of a small quantum system coupled to condensed phase bath is extremely important in chemical physics. We will show how to compute the reduced system density matrix exactly for a large class of “system-bath” Hamiltonians, namely those for which the system Hamiltonian and the system factor in the system-bath coupling term commute. For this class of problems, the Markovian limit of the equations of motion form a positive semigroup and local second order perturbation theory is exact, even for strong system-bath coupling.

An analytically solvable model of a multi-level condensed phase quantum system relevant to vibrational relaxation and electron transfer is presented. Exact solutions are derived for the reduced system density matrix dynamics of a degenerate N-level quantum system coupled to a dissipative harmonic oscillator bath. We demonstrate that for N>2 the long-time steady state system site occupation probabilities are distributed in a non-Boltzmann manner which depends on the initial conditions and the number of levels in the system. These ideas are then applied to an analysis of electron transfer in non-rigid molecular systems where motion of the molecular “bridge” is strongly coupled to the electron transport.