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Jian Wang1, Tian-Xing Liu1, Xiao-Zhi Luo1

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This study reveals anomalous energy diffusion in two-dimensional (2D) momentum-conserved lattices, deviating from 1D systems. Anomalous heat transport in 2D systems is not linked to momentum superdiffusion.

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Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Nonlinear Dynamics

Background:

  • Heat transport in one-dimensional (1D) momentum-conserved lattices is typically anomalous, showing power-law divergence in thermal conductivity.
  • The nature of heat transport in two-dimensional (2D) systems remains debated due to experimental and simulation limitations.

Purpose of the Study:

  • To investigate energy and momentum diffusion in 2D nonlinear lattices.
  • To determine if heat transport in 2D momentum-conserved systems is anomalous.
  • To clarify the relationship between anomalous heat transport and momentum diffusion in 2D systems.

Main Methods:

  • Simulation of energy and momentum diffusion using fluctuation correlation functions.
  • Analysis of diffusion behavior in 2D nonlinear lattices with and without on-site potentials.

Main Results:

  • Energy diffusion in 2D momentum-conserved lattices is confirmed to be anomalous, fitting Lévy-stable distributions.
  • 2D nonlinear lattices with on-site potentials exhibit normal energy diffusion.
  • Anomalous heat transport in 2D momentum-conserved systems is not supported by momentum superdiffusion.

Conclusions:

  • Energy diffusion in 2D momentum-conserved lattices is anomalous, characterized by Lévy-stable distributions.
  • The presence of on-site potentials leads to normal energy diffusion in 2D systems.
  • Momentum superdiffusion does not necessarily indicate anomalous heat transport in 2D momentum-conserved systems.