Slow dissipation and spreading in disordered classical systems: A direct comparison between numerics and mathematical bounds

Abstract

We study the breakdown of Anderson localization in the one-dimensional nonlinear Klein-Gordon chain, a prototypical example of a disordered classical many-body system. A series of numerical works indicate that an initially localized wave packet spreads polynomially in time, while analytical studies rather suggest a much slower spreading. Here, we focus on the decorrelation time in equilibrium. On the one hand, we provide a mathematical theorem establishing that this time is larger than any inverse power law in the effective anharmonicity parameter $\lambda$, and on the other hand our numerics show that it follows a power law for a broad range of values of $\lambda$. This numerical behavior is fully consistent with the power law observed numerically in spreading experiments, and we conclude that the state-of-the-art numerics may well be unable to capture the long-time behavior of such classical disordered systems.

Published version

References in corpus (27)

• Destruction of Anderson localization by a weak nonlinearity
• Universal spreading of wavepackets in disordered nonlinear systems
• Delocalization of wave packets in disordered nonlinear chains
• Energy transport in disordered classical spin chains
• Weak chaos in the disordered nonlinear Schroedinger chain: destruction of Anderson localization by Arnold diffusion
• Delocalization induced by nonlinearity in systems with disorder
• The Nonlinear Schroedinger Equation with a random potential: Results and Puzzles
• Asymptotic quantum many-body localization from thermal disorder
• Spreading of wave packets in disordered systems with tunable nonlinearity
• Universal Nonlinear Disordered Wave Packet Subdiffusion: 12 Decades
• Long time Anderson localization for nonlinear random Schroedinger equation
• KAM tori in 1D random discrete nonlinear Schrödinger model?
• Perturbation theory for the Nonlinear Schroedinger Equation with a random potential
• Characteristics of chaos evolution in one-dimensional disordered nonlinear lattices
• Spreading in Disordered Lattices with Different Nonlinearities
• Subdiffusion of nonlinear waves in quasiperiodic potentials
• Lyapunov spectrum scaling for classical many-body dynamics close to integrability
• Drastic fall-off of the thermal conductivity for disordered lattices in the limit of weak anharmonic interactions
• Decorrelation estimates for the eigenlevels of the discrete Anderson model in the localized regime
• Pre-thermalization in a classical phonon field: slow relaxation of the number of phonons
• Long-time Anderson Localization for the Nonlinear Schrodinger Equation Revisited
• Transport, correlations, and chaos in a classical disordered anharmonic chain
• Quantum subdiffusion with two- and three-body interactions
• On the Joint Distribution of Energy Levels of Random Schroedinger Operators
• Density Resolved Wave Packet Spreading in Disordered Gross-Pitaevskii Lattices
• Enhancement of chaotic subdiffusion in disordered ladders with synthetic gauge fields
• Thermalization of oscillator chains with onsite anharmonicity and comparison with kinetic theory