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Slow dissipation and spreading in disordered classical systems: A direct comparison between numerics and mathematical
Wojciech De Roeck1, Francois Huveneers2, Oskar A Prośniak3
1KU Leuven University, Leuven 3000, Belgium.
Physical Review. E
|May 17, 2024
Summary
We investigated Anderson localization breakdown in a disordered nonlinear system. Our findings show equilibrium decorrelation time is longer than predicted by inverse power laws, suggesting current numerics may miss long-term behavior.
Area of Science:
- Physics
- Condensed Matter Physics
- Nonlinear Dynamics
Background:
- Anderson localization describes wave function confinement in disordered systems.
- The one-dimensional nonlinear Klein-Gordon chain is a key model for disordered classical many-body systems.
- Previous studies show conflicting results on wave packet spreading dynamics.
Purpose of the Study:
- To analyze the decorrelation time in equilibrium for the nonlinear Klein-Gordon chain.
- To reconcile discrepancies between numerical and analytical predictions for wave packet spreading.
- To investigate the long-time behavior of classical disordered systems.
Main Methods:
- Mathematical theorem to establish a lower bound for decorrelation time.
- Numerical simulations to observe system dynamics and decorrelation time.
- Analysis of the effective anharmonicity parameter (λ).
Main Results:
- A mathematical theorem proves decorrelation time exceeds any inverse power law in λ.
- Numerical simulations reveal decorrelation time follows a power law across a wide range of λ.
- Numerical spreading exponents align with the observed power-law behavior.
Conclusions:
- The decorrelation time in equilibrium is theoretically bounded from below by a non-power-law function of λ.
- Numerical results suggest a power-law dependence for decorrelation time, consistent with spreading experiments.
- Current numerical methods may not accurately capture the long-time dynamics of these classical disordered systems.
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