Enhancing the Diffusion in Underdamped Space-Periodic Systems by Applying External Low-Frequency Fields

Abstract

This paper is devoted to the studies of the opportunities for the intensification of the particle diffusion in the periodic structures, for example, the crystals that are exposed to the action of the time-periodic fields of a different nature. These can be acoustic or electromagnetic fields. The trivial one-dimensional model of the motion of the particles in the potential lattice field under the thermal equilibrium has been used. The paper studies the interaction of rectangular fields with the frequencies less than 0.01 ω₀, where ω₀  is the frequency of natural small vibrations of the particles in the systems with the low dissipation. The selected friction coefficient in dimensionless units is equal to γ'=0.03. The amplitude dependence of the intensification of the diffusion D under the action of the fields of a different frequency has been studied. It was shown that the diffusion coefficient can be increased by several orders of magnitude by applying the field of an appropriate amplitude and frequency. A maximum diffusion intensification is attained at ω→0. A maximum attained value of the diffusion coefficient at the periodic force corresponds to the case of the action of the constant force. However, at low frequencies a maximum intensification is only possible in the narrow range of field amplitudes F'oc γ'. A further increase in the field amplitude results in a decrease of the diffusion coefficient and it attains the value of the coefficient of the particle diffusion in the viscous medium D_vis=k'T'/γ', where k'  is the Boltzmann coefficient and T' is the temperature. An increase in the frequency of the external force results in the extension of the range of forces at which D>D_vis, however the value of the diffusion intensification is decreased. It was shown that the exceed of a certain threshold value of the amplitude of the external field  results in the gain of the diffusion coefficient at least by the value of η=(k'T'e^ε/k'T')/(γ"D₀, where ε is the value of the energy barrier during the passage of the particle from one cell of the one-dimensional lattice to another. The obtained data open prospects for the development of new technologies to exercise control over diffusion processes. It is of great importance for the production of nanomaterials with the specified structure, creation of the surface nanostructures, etc.