2-D Breathers and Applications

Abstract

In this chapter we show how a new type of nonlinear lattice excitation is helping to understand the long-standing puzzle of unexplained dark lines in crystals of muscovite mica. In fact, it was the conjecture that some kind of quasi-one-dimensional lattice soliton was responsible for those lines which led to the discovery of this new family of lattice excitations: mobile localized breathers of longitudinal type. We explore several properties of these moving breathers, both by numerical methods and by experimenting with analogue models. The results suggest a much broader application than just the mica problem.

Anomalous Ion Accelerated Bulk Diffusion of Interstitial Nitrogen

“…According to molecular dynamic (MD) simulations, DBs are highly anharmonic longitudinal vibrations, being sharply localized on just a few sites in the longitudional direction and practically across one atomic distance in the transverse direction. Within this oscillation envelope the particles execute antiphase or optical type oscillations [20]. The highly localized excitations on the atomic scale were observed in a quasi-one-dimensional antiferromagnet [21] and atomic lattices [22,23].…”

“…It was shown theoretically that the presence of the surrounding lattice prevents the propagation of Toda-like solitons [18] but allows breatherlike solitons [or so-called discrete breathers (DB)] to propagate along atomic chains [20]. According to molecular dynamic (MD) simulations, DBs are highly anharmonic longitudinal vibrations, being sharply localized on just a few sites in the longitudional direction and practically across one atomic distance in the transverse direction.…”

Impact of intrinsic localized modes of atomic motion on materials properties

“…Subsequent theoretical work lent some support to this idea by showing that it was possible for ILMs to travel over macroscopic distances at specific velocities along certain crystallographic directions [23,24]. A possible connection of this idea to diffusion came with the 1D simulations of Cuevas et al [25] showing that collisions between propagating ILMs and vacancies can cause the vacancies to hop between sites.…”

Numerical Simulations of Nonlinear Modes in Mica: Past, Present and Future

“…This is encouraging, but to demonstrate tracks in mica of centimetres, we need an extra factor of 10 5 in the lifetime. Marín's 2D calculation also included a brief study of inline breather-breather collisions [17]. Most simulations were performed on a 16x16 lattice due to CPU speeds at the time, but a few were done using 32x32 lattices.…”