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Characterization of Thermal Transport in One-dimensional Solid Materials
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Chaotic route to classical thermalization: A real-space analysis.

Yue Liu1, Dahai He1

  • 1Department of Physics and Jiujiang Research Institute, <a href="https://ror.org/00mcjh785">Xiamen University</a>, Xiamen 361005, Fujian, China.

Physical Review. E
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Summary

This study introduces a real-space method to analyze classical thermalization in interacting oscillators, overcoming limitations of wave-vector space approaches. It reveals thermalization time scaling laws and links microscopic chaos to macroscopic thermalization.

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Area of Science:

  • Statistical Mechanics
  • Nonlinear Dynamics
  • Condensed Matter Physics

Background:

  • Classical thermalization studies traditionally focus on wave-vector space, limiting applicability beyond quasi-integrable systems.
  • Investigating thermalization in real space is crucial for understanding systems with complex dynamics.

Purpose of the Study:

  • To propose and validate a novel real-space scheme for studying classical thermalization in interacting oscillator chains.
  • To explore thermalization dynamics in regions beyond quasi-integrability using a real-space approach.

Main Methods:

  • Development of a real-space thermalization indicator based on Parisi's work.
  • Implementation of a quench protocol to create non-equilibrium initial states in a harmonic chain.
  • Numerical simulations on the Fermi-Pasta-Ulam-Tsingou (FPUT)-β lattice.

Main Results:

  • The real-space thermalization indicator approaches zero in the thermal state.
  • Observed thermalization time scaling laws: -2 in the quasi-integrable region and -1/4 in the strongly integrable region of the FPUT-β lattice.
  • Demonstrated proportionality between thermalization time and Lyapunov time.

Conclusions:

  • The proposed real-space method effectively studies thermalization, especially in non-integrable systems.
  • The observed scaling laws provide insights into thermalization dynamics across different integrability regimes.
  • The proportionality to Lyapunov time connects microscopic chaotic behavior to macroscopic thermalization.