| As is well known, the computational effort in quantum mechanics grows exponentially with system size. Thus a typical computation of an interesting many-body problem quickly becomes prohibitive. In this work, we try to circumvent this exponential scaling by treating a few degrees of freedom explicitly (i.e. the system) while integrating out the rest of the degrees of freedom (i.e. the bath). For a bath of harmonic oscillators, this integration procedure is well known and we apply this result to problems of charge transfer across molecules by summing over statistically significant system paths. If we have a generic bath composed of classical like particles interacting with the system of interest, the classical behavior of the bath influences the quantum mechanical behavior of the system. Thus we arrive at a rigorous quantum-classical path integral formulation which we believe has very promising applications in chemistry and biology. |
