Ultradiscrete kinks with supersonic speed in a layered crystal with realistic potentials

Abstract

In this paper we develop a dynamical model of the propagating nonlinear localized excitations, supersonic kinks, in the cation layer in a silicate mica crystal. We start from purely electrostatic Coulomb interaction and add the Ziegler-Biersack-Littmark short-range repulsive potential and the periodic potential produced by other atoms of the lattice. The proposed approach allows the construction of supersonic kinks which can propagate in the lattice within a large range of energies and velocities. Due to the presence of the short-range repulsive component in the potential, the interparticle distances in the lattice kinks with high energy are limited by physically reasonable values. The introduction of the periodic lattice potential results in the important feature that the kinks propagate with the single velocity and single energy, which are independent on the excitation conditions. The unique average velocity of the supersonic kinks on the periodic substrate potential we relate with the kink amplitude of the relative particle displacements, which is determined by the interatomic distance corresponding to the minimum of the total, interparticle plus substrate, lattice potential. The found kinks are ultradiscrete and can be described with the "magic wave number" q = 2π/3a, which was previously revealed in the nonlinear sinusoidal waves and supersonic kinks in the Fermi-Pasta-Ulam lattice. The extreme discreteness of the observed supersonic kinks, with basically two particles moving at the same time, allows the detailed interpretation of their double-kink structure, which is not possible for the multikinks without an account for the lattice discreteness. Analytical calculations of the displacement patterns and energies of the supersonic kinks are confirmed by numerical simulations. The computed energy of the found supersonic kinks in the considered realistic lattice potential is in a good agreement with the experimental evidence for the transport of localized energetic excitations in silicate mica crystals between the points of 40 K recoil and subsequent sputtering.

On the charge of quodons

“…Supersonic lattice kinks have only a discrete set of velocities and energies for which they do not radiate energy. Only one such value has been found in a 1D model for mica muscovite with realistic parameters with 26 eV [9,16].…”

“…As this energy is not available in any decay, this process is not possible, therefore allowing for more recoil energy than proposed in Refs. [9,16].…”

A Supersonic Crowdion in Mica

“…Recently, a model with realistic potentials for the dynamics of potassium ions within the cation layer of mica muscovite has been introduced [1][2][3]. The authors have considered the available potentials for the interaction between atoms and ions.…”

Solitons as candidates for energy carriers in Fermi-Pasta-Ulam lattices

“…(3) permits the bell-shaped soliton solutions for φ j (corresponding to the kink-shaped soliton solutions for u j ) [69,[79][80][81][82][83][84][85][86]. Soliton is a travelling wave solution and can be expressed formally as…”

“…Besides in the continuous nonlinear systems, the existence of solitons in FPU lattices has been proved [74][75][76][77][78]. A series of numerical works have directly observed solitons in FPU lattices [69,[79][80][81][82][83][84][85][86]. Therefore, solitons were naturally supposed to be the energy carriers in the nonlinear momentum-conserving lattices [22,[53][54][55][56][57][58][59].…”