Heat Conduction in One-Dimensional chain of Hard Discs with Substrate Potential

TL;DR

This paper investigates heat conduction in a one-dimensional chain of hard discs with an external substrate potential, demonstrating that nonzero particle sizes lead to finite heat conduction coefficients, confirmed by analytical and numerical methods.

Contribution

It introduces an analytical model showing how nonzero particle sizes break integrability and result in finite heat conduction, supported by numerical verification.

Findings

Nonzero particle size leads to finite heat conduction coefficient.

Integrability is preserved only at zero particle diameter.

Analytical results agree with numerical simulations.

Abstract

Heat conduction of one-dimensional chain of equivalent rigid particles in the field of external on-site potential is considered. Zero diameters of the particles correspond to exactly integrable case with divergent heat conduction coefficient. By means of simple analytical model it is demonstrated that for any nonzero particle size the integrability is violated and the heat conduction coefficient converges. The result of the analytical computation is verified by means of numerical simulation in a plausible diapason of parameters and good agreement is observed