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

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.

5 pages, 4 figures

References in corpus (8)

• Destruction of Anderson localization by a weak nonlinearity
• Universal spreading of wavepackets in disordered nonlinear systems
• Absence of Wavepacket Diffusion in Disordered Nonlinear Systems
• Wave function mapping in graphene quantum dots with soft confinement
• Quantum confined electronic states in atomically well-defined graphene nanostructures
• Spatiotemporal vortex solitons in hexagonal arrays of waveguides
• Discrete solitons and vortices in hexagonal and honeycomb lattices: Existence, stability, and dynamics
• Stability and decay of Bloch oscillations in presence of time-dependent nonlinearity