Finite thermal conductivity in 1D lattices

Area of Science:

• Physics
• Condensed Matter Physics
• Statistical Mechanics

Background:

• Understanding thermal transport in one-dimensional (1D) nonlinear systems is crucial for various fields.
• Previous models often required on-site potentials to exhibit normal transport properties.
• The behavior of heat diffusion in nonlinear lattices remains an active area of research.

Purpose of the Study:

• To investigate the thermal conductivity of a 1D nonlinear lattice of coupled rotators.
• To determine if normal transport properties can be observed in the absence of an on-site potential.
• To provide numerical and theoretical evidence for energy diffusion mechanisms.

Main Methods:

• Simulating a chain of coupled rotators in contact with two thermal baths at different temperatures.
• Employing linear response theory to estimate thermal conductivity.
• Analyzing the dynamics of Fourier modes to observe energy diffusion.
• Examining two variants of the model to confirm findings.

Main Results:

• The coupled rotator chain is identified as the first 1D nonlinear lattice exhibiting normal transport without an on-site potential.
• Numerical estimates for thermal conductivity align with predictions from linear response theory.
• Direct evidence of energy diffusion was observed through the dynamics of Fourier modes.
• The finiteness of thermal conductivity was attributed to the occurrence of phase jumps.

Conclusions:

• The coupled rotator model provides a fundamental example of normal heat transport in a 1D nonlinear system.
• Phase jumps are identified as the critical factor limiting thermal conductivity in this model.
• The findings are robust and confirmed by analyzing model variants.