Sub-Power Law Decay of the Wave Packet Maximum in Disordered Anharmonic Chains

2025/02/04 by De Roeck, Wojciech, Giacomin, Lydia, Hannani, Amirali +1
#Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2502.02344

Abstract

We show that the peak of an initially localized wave packet in one-dimensional nonlinear disordered chains decays more slowly than any power law of time. The systems under investigation are Klein-Gordon and nonlinear disordered Schrödinger-type chains, characterized by a harmonic onsite disordered potential and quartic nearest-neighbor coupling. Our results apply in the long-time limit, hold almost surely, and are valid for arbitrary finite energy values.

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