Thermal gauge potentials and coherent thermally assisted tunnelling

Abstract

It is commonly assumed that thermal excitation of a vibration leads to an incoherent mixture of vibrational states. The author shows using the excitation of a violin string by a steadily driven bow as a model, that the new gauge theory of driven dynamical systems implies coherence. This means that the thermally excited state is a pure one in a representation that moves with the vibrations. This gives rise to a new and very simple description of thermally assisted tunnelling through the barriers of a periodic potential. It explains why there is only a single transport process, not one for each vibrational level. The real and imaginary parts correspond to the free bidirectional tunnelling frequency and to the thermally driven monodirectional tunnelling rate. A simple statistical mechanical assumption enables both of these to be easily obtained as weighted averages of overlap integrals of vibrational states located in adjacent potential wells. As the coherent tunnelling frequency declines with increasing temperature and the thermally driven rate rapidly increases, a smooth transition occurs from the quantum tunnelling regime to a quasi-classical thermal hopping regime. The predictions are in good agreement with a large body of experimental data on quantum tunnelling and thermally activated rotations of methyl groups. The general assumptions are expected to apply to some degree to other transport phenomena.