Stretch diffusion and heat conduction in 1D nonlinear lattices

TL;DR

This paper investigates how conserved quantities like stretch and momentum influence heat conduction in 1D nonlinear lattices, revealing that the relationship is more complex than previously suggested.

Contribution

It systematically examines stretch diffusion in typical 1D nonlinear lattices, challenging prior claims about conserved quantities and heat conduction.

Findings

No clear link between conserved quantities and heat conduction.

The relationship between stretch, momentum, and heat conduction is more complex than previously thought.

Previous assumptions about normal diffusion linked to conserved quantities are not universally valid.

Abstract

In the study of 1D nonlinear Hamiltonian lattices, the conserved quantities play an important role in determining the actual behavior of heat conduction. Besides the total energy, total momentum and total stretch could also be conserved quantities. In microcanonical Hamiltonian dynamics, the total energy is always conserved. It was recently argued by Das and Dhar that whenever stretch (momentum) is not conserved in a 1D model, the momentum (stretch) and energy fields exhibit normal diffusion. In this work, we will systematically investigate the stretch diffusions for typical 1D nonlinear lattices. No clear connection between the conserved quantities and heat conduction can be established. The actual situation is more complicated than what Das and Dhar claimed.