Delocalization and spreading in a nonlinear Stark ladder

Details Delocalization and spreading in a nonlinear Stark ladder Delocalization and spreading in a nonlinear Stark ladder

2009-04-18

arxiv.org/abs/0904.2867v1

Phys. Rev. E 80, 036201 (2009)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 5 figures

Scientific paper

10.1103/PhysRevE.80.036201

We study the evolution of a wave packet in a nonlinear Schr\"odinger lattice equation subject to a dc bias. In the absence of nonlinearity all normal modes are spatially localized giving rise to a Stark ladder with an equidistant eigenvalue spectrum and Bloch oscillations. Nonlinearity induces frequency shifts and mode-mode interactions and destroys localization. With increasing strength of nonlinearity we observe: (I) localization as a transient, with subsequent subdiffusion (weak mode-mode interactions); (II) immediate subdiffusion (strong mode-mode interactions); (III) single site trapping as a transient, with subsequent explosive spreading, followed by subdiffusion. For single mode excitations and weak nonlinearities stability intervals are predicted and observed upon variation of the dc bias strength, which affect the short and long time dynamics.

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