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 role of anomalous conduction in coupled transport and describe how systems with anomalous (thermal) diffusion allow a much better power-efficiency trade-off for the conversion of thermal to particle current.

Finite-temperature transport in one-dimensional quantum lattice models

“…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.…”

Ultrahigh Convergent Thermal Conductivity of Carbon Nanotubes from Comprehensive Atomistic Modeling

“…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].…”

Hydrodynamics and transport in the long-range-interacting $φ^4$ chain

“…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].…”