2020
DOI: 10.3389/fphy.2020.00292
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Anomalous Heat Transport in Classical Many-Body Systems: Overview and Perspectives

Abstract: In this review paper we survey recent achievements in anomalous heat diffusion, while highlighting open problems and research perspectives. First, we briefly recall the main features of the phenomenon in low-dimensional classical anharmonic chains and outline some recent developments in the study of perturbed integrable systems and the effect of long-range forces and magnetic fields. Selected applications to heat transfer in material science at the nanoscale are described. In the second part, we discuss of the… Show more

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Cited by 49 publications
(39 citation statements)
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References 124 publications
(173 reference statements)
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“…Such a distinction, however, is not as clearcut as one might think. While no rigorous conclusions have been reached yet [for reviews, see (Benenti et al, 2020;Dhar, 2008;Lepri et al, 2003)], explicit examples demonstrate that even systems without classical chaos can display a wide spectrum of transport types.…”
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confidence: 99%
“…Such a distinction, however, is not as clearcut as one might think. While no rigorous conclusions have been reached yet [for reviews, see (Benenti et al, 2020;Dhar, 2008;Lepri et al, 2003)], explicit examples demonstrate that even systems without classical chaos can display a wide spectrum of transport types.…”
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confidence: 99%
“…While in standard bulk materials heat diffusion obeys Fourier's law and the thermal conductivity κ is an intrinsic property, the thermal conductivity of the FPU and other 1D models diverges with their length L as κ ∼ L α , with α > 0 [2,3]. Heat transport in these models is deemed anomalous, as it violates the principles of normal diffusion [4][5][6][7][8][9][10].…”
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confidence: 99%
“…This is justified by the fact that macroscopic fluctuations of conserved quantities (and order parameters close to criticality) must evolve slowly with respect to microscopic time-scales to reach a steady state. If the relevant correlations have long-time tails, standard diffusive behavior may break down as it happens generically in nonlinear, low-dimensional systems [1,2,3,4]. Anomalous transport in such many-body systems can be effectively described by a random Lévy walk [5] of the energy carriers, as demonstrated extensively in the literature [6,7,8].…”
Section: Introductionmentioning
confidence: 98%