Wavepacket spreading dynamics under a non-instantaneous nonlinearity: Self-trapping, defocusing and focusing

TL;DR

This paper investigates how a non-instantaneous nonlinear response affects wavepacket spreading and localization, revealing complex dynamics and phase diagrams in systems modeled by a nonlinear Schrödinger equation with relaxation.

Contribution

It introduces the impact of non-instantaneous nonlinearity relaxation on wavepacket dynamics, a novel aspect not considered in traditional models assuming instantaneous response.

Findings

Relaxation of nonlinearity significantly alters wavepacket spreading.

Complex phase diagrams emerge due to non-instantaneous nonlinear effects.

Localized modes and self-trapping phenomena are affected by the relaxation process.

Abstract

Special localized wavemodes show up in several physical scenarios including BEC in optical lattices, nonlinear photonic crystals and systems with strong electron-phonon interaction. These result from an underlying nonlinear contribution to the wave equation that is usually assumed to be instantaneous. Here we demonstrate that the relaxation process of the nonlinearity has a profound impact in the wavepacket dynamics and in the formation of localized modes. We illustrate this phenomenology by considering the one-electron wavepacket spreading in a $C60$ buckball structure whose dynamics is governed by a discrete nonlinear Schroedinger equation with a Debye relaxation of the nonlinearity. We report the full phase-diagram related to the spacial extension of the asymptotic wavepacket and unveil a complex wavepacket dynamical behavior.