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Related Experiment Video

Updated: Jun 14, 2026

Measuring the Time-Evolution of Nanoscale Materials with Stopped-Flow and Small-Angle Neutron Scattering
07:53

Measuring the Time-Evolution of Nanoscale Materials with Stopped-Flow and Small-Angle Neutron Scattering

Published on: August 6, 2021

Random Initial Data and Average Shock Time in the Fermi-Pasta-Ulam-Tsingou Chain.

Matteo Gallone1, Ricardo Grande1, Antonio Ponno2

  • 1Scuola Internazionale di Studi Superiori Avanzati, Via Bonomea 265, 34136 Trieste, Italy.

Physical Review Letters
|June 12, 2026
PubMed
Summary
This summary is machine-generated.

The Fermi-Pasta-Ulam-Tsingou chain exhibits prethermalization with small energy, forming a shock and turbulent spectrum. This prethermal state is robust, with shock time scaling intensively with excited modes.

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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

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Related Experiment Videos

Last Updated: Jun 14, 2026

Measuring the Time-Evolution of Nanoscale Materials with Stopped-Flow and Small-Angle Neutron Scattering
07:53

Measuring the Time-Evolution of Nanoscale Materials with Stopped-Flow and Small-Angle Neutron Scattering

Published on: August 6, 2021

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Area of Science:

  • Nonlinear dynamics
  • Statistical physics
  • Condensed matter physics

Background:

  • The Fermi-Pasta-Ulam-Tsingou (FPU) chain is a fundamental model for studying nonlinear lattice dynamics and the approach to thermal equilibrium.
  • Understanding prethermalization is crucial for systems that do not rapidly reach thermal equilibrium.
  • Previous studies have explored FPU dynamics, but the robustness of prethermalization under generic random initial conditions requires further investigation.

Purpose of the Study:

  • To investigate the dynamics of the FPU chain with long-wavelength random initial data.
  • To characterize the formation and robustness of the prethermal state.
  • To derive a precise mathematical expression for the average shock time.

Main Methods:

  • Analysis of the FPU chain dynamics under long-wavelength random initial conditions.
  • Identification of Burgers-type shock formation and turbulentlike spectrum.
  • Application of advanced probabilistic techniques (Dudley, Talagrand) to derive asymptotic expressions.
  • Thermodynamic limit analysis for large systems.

Main Results:

  • Demonstration that prethermalization, Burgers-type shock, and turbulentlike spectrum are robust under generic long-wavelength random initial conditions.
  • Derivation of a sharp asymptotic expression for the average shock time in the thermodynamic limit.
  • Proof that the shock time scales as (psqrt[logp])^{-1} for large p (number of excited modes), indicating it is an intensive quantity with logarithmic corrections.

Conclusions:

  • The prethermal state in the FPU chain is a robust phenomenon under generic random initial conditions.
  • The derived shock time scaling provides a quantitative understanding of prethermalization dynamics.
  • These findings advance the understanding of thermalization processes in nonlinear systems.