Burgers Turbulence in the Fermi-Pasta-Ulam-Tsingou Chain

Area of Science:

• Nonlinear dynamics
• Statistical mechanics
• Condensed matter physics

Background:

• The Fermi-Pasta-Ulam-Tsingou (FPUT) chain is a fundamental model for studying energy transfer and thermalization in nonlinear systems.
• Understanding the pathways to thermalization in conservative systems is a long-standing challenge in physics.

Purpose of the Study:

• To analytically and numerically investigate the dynamics of the FPUT chain.
• To identify the transient regimes governing energy equipartition and thermalization.

Main Methods:

• Analytical proofs and numerical simulations of the FPUT chain dynamics.
• Perturbative calculations of the energy spectrum at small energy per particle.
• Analysis using generalized Burgers equations to model shock formation.

Main Results:

• A transient Burgers turbulence regime is identified, preceding thermalization.
• Shock formation, predictable by generalized Burgers equations, drives the system towards thermalization.
• The energy spectrum E_{k} exhibits a power-law decay E_{k}∼k^{-ζ(t)}, with ζ(t) evolving from 8/3 to approximately 2.
• An exponential cutoff at large wavenumbers (k) is observed, consistent with previous findings.

Conclusions:

• The FPUT chain dynamics are characterized by a universal transient Burgers turbulence regime.
• Shock dynamics play a crucial role in the energy cascade and approach to thermalization.
• The observed spectral behavior and its universality provide insights into energy transport in nonlinear systems.