Temperature Effects on the Davydov Soliton

Abstract

There are two effects which tend to delocalize the Davydov soliton. First, quantum fluctuations which can also be seen as a zero point motion of the soliton position. Second, thermal fluctuations produced by the interaction with the surrounding solvent. This solvent, which we now call heatbath, wants to force the system into thermal equilibrium. We discuss under what circumstances a soliton in the Alpha-helix can be seen as a thermodynamic equilibrium state. We show how the principle of a minimal free energy, formulated in a variational principle of thermodynamics, can be used to optimize a given ansatz for the density operator. Thermal soliton theories of Davydov and Krumhansl are discussed within this theory. Both, in principle, use the same ansatz with no freedom to adjust for maximum entropy. In using a more realistic ansatz, we always get the result that the soliton is delocalized. Finally, we discuss how the strength of interaction, together with the internal structure of the heatbath, determines the thermal lifetime of the soliton.