Nonlinear Wave-Packet Dynamics in a Disordered Medium

Nonlinear wave-packet dynamics in a disordered medium.

We develop an effective theory of pulse propagation in a nonlinear and disordered medium in two dimensions. The theory is formulated in terms of a nonlinear diffusion equation. Despite its apparent simplicity this equation describes novel phenomena which we refer to as "locked explosion" and diffusive collapse. The equation can be applied to such distinct physical systems as laser beams propaga...

Absence of wave packet diffusion in disordered nonlinear systems.

We study the spreading of an initially localized wave packet in two nonlinear chains (discrete nonlinear Schrödinger and quartic Klein-Gordon) with disorder. Previous studies suggest that there are many initial conditions such that the second moment of the norm and energy density distributions diverges with time. We find that the participation number of a wave packet does not diverge simultaneo...

Localization of a matter wave packet in a disordered potential

Asymptotic energy profile of a wave packet in disordered chains.

We investigate the long-time behavior of a wave packet initially localized at a single site n₀ in translationally invariant harmonic and anharmonic chains with random interactions. In the harmonic case, the energy profile averaged on time and disorder decays for large |n-n₀| as a power law ≈ C|n-n₀|(⁻η), where η=⁵/₂ and ³/₂ for initial displacement and momentum excitations, ...

Evolution of a vibrational wave packet on a disordered chain

A linear chain of point masses coupled by harmonic springs is a standard model used to introduce concepts of solid state physics. The well-ordered chain has sinusoidal standing wave normal modes ~if the ends are fixed! or traveling wave normal modes ~if the ends are connected in a ring!. Ballistically propagating wave packets can be built from these normal modes, and illustrate the mechanism of...