Anomalous heat transport in classical many-body systems: overview and perspectives

Abstract

In this review paper we aim at illustrating recent achievements in anomalous heat diffusion, while highlighting open problems and research perspectives. We briefly recall the main features of the phenomenon for low-dimensional classical anharmonic chains and outline some recent developments on perturbed integrable systems, and on the effect of long-range forces and magnetic fields. Some 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 on 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.

Review article, in Anomalous Transport: Applications, Mathematical Perspectives, and Big Data edited by R. Metzler, C. Mejia-Monasterio and J. Voellmer

References in corpus (26)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• Heat Transport in low-dimensional systems
• Lévy walks
• A momentum conserving model with anomalous thermal conductivity in low dimension
• Finding the quantum thermoelectric with maximal efficiency and minimal entropy production at given power output
• Operationally accessible bounds on fluctuations and entropy production in periodically driven systems
• Fourier's Law in a Quantum Spin Chain and the Onset of Quantum Chaos
• Thermal transport of the XXZ chain in a magnetic field
• Non-integrability and the Fourier heat conduction law
• Anomalous energy transport in the FPU-beta chain
• Functional Integral approach to time-dependent heat exchange in open quantum systems: general method and applications
• The nonequilibrium discrete nonlinear Schroedinger equation
• Anomalous heat transport in one dimensional systems: a description using non-local fractional-type diffusion equation
• Thermal transport in the Fermi-Pasta-Ulam model with long-range interactions
• Spreading of Perturbations in Long-Range Interacting Classical Lattice Models
• Equilibrium dynamical correlations in the Toda chain and other integrable models
• Non-diffusive Lattice Thermal Transport in Si-Ge Alloy Nanowires
• Heat Transport in Quantum Spin Chains: Stochastic Baths vs Quantum Trajectories
• A microscopic mechanism for increasing thermoelectric efficiency
• Conservation Laws and Thermodynamic Efficiencies
• Heat transport via low-dimensional systems with broken time-reversal symmetry
• Equilibrium time-correlation functions of the long-range interacting Fermi-Pasta-Ulam model
• Transport properties of the classical Toda chain: effect of a pinning potential
• Surprises from quenches in long-range interacting systems: Temperature inversion and cooling
• Transport in one dimensional quantum systems
• Fluctuating hydrodynamics for a chain of nonlinearly coupled rotators

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• Stochastic thermodynamics of inertial-like Stuart-Landau dimer
• Kinetic and hydrodynamic regimes in multi-particle-collision dynamics of a one-dimensional fluid with thermal walls
• Conformal order and Poincar$\acute{\mathrm{e}}$-Klein mapping underlying electrostatics-driven inhomogeneity in tethered membranes
• Hydrodynamics and transport in the long-range-interacting ${\phi }^4$ chain
• Non-equilibrium steady states of long-range coupled harmonic chains
• Analysis of ballistic transport and resonance in the $\alpha$-Fermi-Pasta-Ulam-Tsingou model
• Thermalization of isolated harmonic networks under conservative noise
• Autonomous Circular Heat Engine
• Heat transport and cooling performance in a nanomechanical system with local and non local interactions
• Fractional Dynamics and Modulational Instability in Long-Range Heisenberg Chains
• Thermal transport in long-range interacting harmonic chains perturbed by long-range conservative noise
• Construction of cubic nonlinear lattice free from umklapp processes
• Classical and quantum harmonic mean-field models coupled intensively and extensively with external baths