Dynamics of a mixed quantum-classical system at finite temperature

The Davydov model for energy storage and transport in proteins is used to illustrate the problems associated with the thermalisation of mixed quantum-classical systems. A new system of equations of motion is proposed, which leads to the correct statistics and is exact in the adiabatic limit. The dynamics of the semiclassical Davydov model at finite temperature given by the present theory is compared with that obtained by the classical Langevin approach. At biological temperatures, while the classical Langevin dynamics predicts a rapid spread of an initially localised excitation, the semiclassical dynamics predicts a stochastic hopping of a localised excitation and an average localisation 75% at equilibrium.