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Updated: Mar 12, 2026

Characterization of Thermal Transport in One-dimensional Solid Materials
Published on: January 26, 2014
Role of the range of the interactions in thermal conduction
Carlos Olivares1, Celia Anteneodo1,2
1Department of Physics, PUC-Rio, Rio de Janeiro, Brazil.
Abstract:
We investigate thermal transport along a one-dimensional lattice of classical inertial rotators, with attractive couplings that decrease with distance as r^{-α} (α≥0), subject at its ends to Brownian heat reservoirs at different temperatures with average value T. By means of numerical integration of the equations of motion, we show the effects of the range of the interactions in the temperature profile and energy transport and determine the domain of validity of Fourier's law in this context. We find that Fourier's law, as signaled by a finite κ in the thermodynamic limit, holds only for sufficiently short-range interactions, with α>α_{c}(T). For α<α_{c}(T), a kind of insulator behavior emerges at any T.
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