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Characterization of Thermal Transport in One-dimensional Solid Materials
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Thermalization in the one-dimensional Salerno model lattice.

Thudiyangal Mithun1, Aleksandra Maluckov2,3, Bertin Many Manda4

  • 1Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA.

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|April 17, 2021
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Summary

This study explores the statistical mechanics of the Salerno model, revealing how varying parameters expand thermalization regions. Finite system size significantly impacts thermalization in non-Gibbs regimes.

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Area of Science:

  • Statistical mechanics
  • Nonlinear physics
  • Condensed matter theory

Background:

  • The Salerno model interpolates between integrable (Ablowitz-Ladik) and nonintegrable (discrete nonlinear Schrödinger) models.
  • Thermalization is governed by the interplay of local on-site nonlinearity and nonlinear dispersion.

Purpose of the Study:

  • Investigate the statistical mechanics of the 1D Salerno lattice in the nonintegrable regime.
  • Illustrate thermalization within the Gibbs regime.
  • Analyze the impact of varying interpolation parameters on thermalization.

Main Methods:

  • Statistical mechanics analysis.
  • Direct numerical computations for finite systems.
  • Exploration of different parametric regimes.

Main Results:

  • The region leading to thermalization expands as the parameter shifts from DNLS towards AL.
  • Thermalization in the non-Gibbs regime is highly dependent on finite system size.
  • Demonstration of thermalization in the Gibbs regime.

Conclusions:

  • The Salerno model exhibits complex thermalization dynamics influenced by nonlinearity, dispersion, and system parameters.
  • Finite-size effects are crucial for understanding thermalization in non-Gibbs regimes.
  • The study provides insights into the statistical mechanics of interpolating nonlinear lattice models.