Heat conduction in chains of non-locally coupled harmonic oscillators: mean-field limit

Abstract

We consider one-dimensional systems of all-to-all harmonically coupled particles with arbitrary masses, subject to two Langevin thermal baths. The couplings correspond to the mean-field limit of long-range interactions. Additionally, the particles can be subject to a harmonic on-site potential to break momentum conservation. Using the non-equilibrium Green operator formalism, we calculate the transmittance, the heat flow and local temperatures, for arbitrary configurations of masses. For identical masses, we show analytically that, the heat flux decays with the system size $N$, as $1/N$, regardless of the conservation or not of the momentum, and of the introduction or not of a Kac factor. These results describe in good agreement the thermal behavior of systems with small heterogeneity in the masses.

6 pages, 5 figures

References in corpus (11)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• Heat Transport in low-dimensional systems
• Thermal rectification and negative differential thermal resistance in lattices with mass gradient
• On the diffusive anomalies in a long-range Hamiltonian system
• Anomalous heat transport in classical many-body systems: overview and perspectives
• Thermal transport in the Fermi-Pasta-Ulam model with long-range interactions
• 1D momentum-conserving systems: the conundrum of anomalous versus normal heat transport
• Energy transport in the presence of long-range interactions
• Equilibrium time-correlation functions of the long-range interacting Fermi-Pasta-Ulam model
• Heat transport in long-ranged anharmonic oscillator models
• Localization effects due to a random magnetic field on heat transport in a harmonic chain

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• Recent progress on thermal transport in one-dimensional long-range interacting Fermi-Pasta-Ulam-Tsingou lattice systems
• Classical and quantum harmonic mean-field models coupled intensively and extensively with external baths