Double Scaling in the Relaxation Time in the β-Fermi-Pasta-Ulam-Tsingou Model.
Yuri V Lvov1, Miguel Onorato2,3
1Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, New York 12180, USA.
Physical Review Letters
|April 26, 2018
Summary
The Fermi-Pasta-Ulam-Tsingou system reaches equilibrium regardless of initial energy. Thermalization time scales change with nonlinearity, supporting the Chirikov overlap criterion for relaxation transitions.
Area of Science:
- Nonlinear dynamics
- Statistical mechanics
- Computational physics
Background:
- The Fermi-Pasta-Ulam-Tsingou (FPUT) problem investigates energy redistribution in nonlinear systems.
- Previous studies suggest FPUT systems reach statistical equilibrium, but thermalization timescales remain debated.
Purpose of the Study:
- To numerically estimate the equipartition timescale in the FPUT system.
- To investigate the influence of nonlinearity on thermalization time scales.
- To validate the Chirikov overlap criterion's role in relaxation dynamics.
Main Methods:
- Numerical simulations of the FPUT system with ensemble averages over initial conditions.
- Analysis of wave-wave resonant interactions.
- Derivation of a formula for nonlinear frequency broadening.
Main Results:
- Equilibration is achieved independently of initial energy for finite systems.
- For weak nonlinearity, equipartition timescales match predictions from resonant wave-wave interaction theory.
- A distinct scaling for thermalization time is observed when frequency overlap occurs.
Conclusions:
- The Chirikov overlap criterion signifies a transition between different relaxation time scalings in the FPUT system.
- Results support the theoretical understanding of thermalization in nonlinear systems.
- Nonlinear frequency broadening plays a crucial role in system dynamics and relaxation.
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