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Heat transport in oscillator chains with long-range interactions coupled to thermal reservoirs

Stefano Iubini1,2,*, Pierfrancesco Di Cintio3,2, Stefano Lepri4,2, Roberto Livi1,2,4, and Lapo Casetti1,2,5

  • 1Dipartimento di Fisica e Astronomia and CSDC, Università di Firenze, via G. Sansone 1 I-50019 Sesto Fiorentino, Italy
  • 2Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, via G. Sansone 1 I-50019 Sesto Fiorentino, Italy
  • 3Consiglio Nazionale delle Ricerche, Istituto di Fisica Applicata “Nello Carrara,” via Madonna del Piano 10 I-50019 Sesto Fiorentino, Italy
  • 4Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, via Madonna del Piano 10 I-50019 Sesto Fiorentino, Italy
  • 5INAF, Osservatorio Astrofisico di Arcetri, largo Enrico Fermi 5, I-50125 Firenze, Italy

  • *stefano.iubini@unifi.it
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Phys. Rev. E 97, 032102 – Published 5 March, 2018

DOI: https://doi.org/10.1103/PhysRevE.97.032102

Abstract

We investigate thermal conduction in arrays of long-range interacting rotors and Fermi-Pasta-Ulam (FPU) oscillators coupled to two reservoirs at different temperatures. The strength of the interaction between two lattice sites decays as a power α of the inverse of their distance. We point out the necessity of distinguishing between energy flows towards or from the reservoirs and those within the system. We show that energy flow between the reservoirs occurs via a direct transfer induced by long-range couplings and a diffusive process through the chain. To this aim, we introduce a decomposition of the steady-state heat current that explicitly accounts for such direct transfer of energy between the reservoir. For 0≤α<1, the direct transfer term dominates, meaning that the system can be effectively described as a set of oscillators each interacting with the thermal baths. Also, the heat current exchanged with the reservoirs depends on the size of the thermalized regions: In the case in which such size is proportional to the system size N, the stationary current is independent on N. For α>1, heat transport mostly occurs through diffusion along the chain: For the rotors transport is normal, while for FPU the data are compatible with an anomalous diffusion, possibly with an α-dependent characteristic exponent.

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Phys. Rev. E 97, 032102– Published 5 March, 2018
  • Received 21 December 2017
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