QUANTUM AND TEMPERATURE EFFECTS ON DAVYDOV SOLITON DYNAMICS .4. LATTICE WITH A THERMAL PHONON DISTRIBUTION

We derive equations of motion for a new model to introduce temperature effects into Davydov's \D1] theory for solitons in proteins. The temperature model used so far suffers from conceptual difficulties, although it can reproduce exact quantum Monte Carlo (QMC) results qualitatively correctly as was shown in part II of this series. In our model we populate the lattice with a thermal phonon distribution and derive equations of motion in the presence of these thermal phonons, instead of deriving equations of motion from a thermally averaged Hamiltonian as in Davydov's theory. This procedure seems to be more reliable than Davydov's averaged Hamiltonian approach. For derivation of the equations of motion the Euler-Lagrange method is used. Numerical applications to soliton dynamics at 300 K are reported and comparisons of the results obtained with available exact QMC data are discussed. It is found that Davydov's method agrees better with the Qmc results than does the newly derived method, although the latter method seems to be physically more reliable.