Known and less known about the Wave of Translation, Davydov’s soliton and its dynamics in an oscillating magnetic field

Abstract

Some less-known facts of the Wave of Translation discovery and a brief review of the advancement of the theory of Davydov’s solitons are given. Dynamics of the Davydov’s soliton in an external oscillating in time magnetic field is investigated. The analysis shows that soliton wave function is a superposition of the electron plane wave in the plane perpendicular to the molecular chain, and longitudinal component of the wave function, which satisfies the modified Nonlinear Schrödinger equation. It is shown that soliton width and amplitude are constant, while its velocity and phase are oscillating in time functions with the frequency of the main harmonic determined by the magnetic field frequency. Furthermore, in the presence of the energy dissipation, soliton velocity is bound from above due to the balance of the energy gain from the magnetic field, and its loss because of the radiation of linear sound waves and energy dissipation. Soliton radiation due to time-depending velocity is calculated and shown to be the most intensive at the resonant frequency of the magnetic field. Such complex impact of time-depending magnetic fields on charge transport, provided by solitons, can affect functioning of the devices based on low-dimensional molecular systems. These results suggest the physical mechanism of the resonant therapeutic effects of oscillating magnetic fields as the resonant impact of the magnetic field on the dynamics of solitons, which provide charge transport along biological macromolecules in the redox processes.