Dynamics of the Davydov’s soliton in external oscillating magnetic field

The influence of an external oscillating in time magnetic field on the dynamics of the Davydov’s soliton is studied. It is shown that soliton parameters depend on the amplitude and frequency of the magnetic field, as well as on the field orientation with respect to the molecular chain axis. Electron dynamics in the parallel magnetic field is a composition of the “free” soliton coherent propagation along the molecular chain and oscillatory movement in the transverse direction. The latter is described by the functions of the harmonic oscillator with the cyclotron frequency depending on the field frequency. In a perpendicular field the soliton dynamics is a superposition of (i) the free electron plane wave in the plane perpendicular to the molecular chain, and (ii) propagation along the chain which is described by the modified Nonlinear Schrödinger equation with an extra term depending on the field. This equation is solved using the nonlinear perturbation theory. It is shown that the soliton velocity and phase are given by expressions which include the terms oscillating in time with the frequency of the main harmonic, given by the external field frequency, and higher multiple harmonics. Such complex effects of external time-depending magnetic fields on the dynamics of solitons modify the charge transport in low-dimensional molecular systems, which in its turn, can affect the functioning of the devices based on such compounds. These results suggest also the physical mechanism of therapeutic effects of oscillating magnetic fields, based on the field influence on the dynamics of solitons which provide charge transport through biological macromolecules in the redox processes.