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