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Chaos and Anderson localization in disordered classical chains: Hertzian versus Fermi-Pasta-Ulam-Tsingou models
A Ngapasare1, G Theocharis1, O Richoux1
1Laboratoire d'Acoustique de l'Université du Maine, UMR CNRS 6613 Av. O. Messiaen, F-72085 LE MANS Cedex 9, France.
Physical Review. E
|April 20, 2019
Summary
Disordered granular chains exhibit unique energy spreading due to discontinuous nonlinearity, transitioning from Anderson localization to equipartition. The Fermi-Pasta-Ulam-Tsingou model shows energy-dependent chaotic dynamics.
Area of Science:
- Nonlinear dynamics
- Condensed matter physics
- Statistical mechanics
Background:
- Anderson localization describes wave function confinement in disordered systems.
- Fermi-Pasta-Ulam-Tsingou (FPUT) models explore energy dynamics in nonlinear lattices.
- Granular chains possess discontinuous nonlinearity when particle contacts break.
Purpose of the Study:
- Investigate the role of discontinuous nonlinearity in Anderson localization.
- Analyze the chaotic dynamics of disordered 1D lattices.
- Compare Hertzian granular chains with FPUT models.
Main Methods:
- Numerical simulations of disordered 1D lattices.
- Utilized Hertzian and FPUT models.
- Analyzed particle displacements and energy propagation.
Main Results:
- Identified three dynamic regimes: localization without chaos, localization with chaos, and energy spreading with chaos/equipartition.
- Hertzian model shows discontinuous nonlinearity triggers energy spreading at lower energies.
- Hertzian chain transitions from Anderson localization to equipartition via nonlinearity propagation; FPUT exhibits energy-dependent localized/delocalized chaotic behavior.
Conclusions:
- Discontinuous nonlinearity is crucial for energy spreading and overcoming Anderson localization in granular chains.
- The Hertzian model's unique nonlinearity drives a transition to equipartition.
- FPUT model dynamics are sensitive to initial energy, showing a complex interplay of localization and chaos.
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