Heat transport in low dimensions: introduction and phenomenology

Abstract

In this chapter we introduce some of the basic models and concepts that will be discussed throughout the volume. In particular we describe systems of nonlinear oscillators arranged on low-dimensional lattices and summarize the phenomenology of their transport properties.

Review paper, to appear in the Springer Lecture Notes in Physics volume "Thermal transport in low dimensions: from statistical physics to nanoscale heat transfer" (S. Lepri ed.)

References in corpus (8)

• A momentum conserving model with anomalous thermal conductivity in low dimension
• Numerical test of hydrodynamic fluctuation theory in the Fermi-Pasta-Ulam chain
• Self-Consistent Mode-Coupling Approach to 1D Heat Transport
• Energy diffusion in hard-point systems
• A violation of universality in anomalous Fourier's law
• Detailed Examination of Transport Coefficients in Cubic-Plus-Quartic Oscillator Chains
• A microscopic mechanism for increasing thermoelectric efficiency
• Nonequilibrium Invariant Measure under Heat Flow

Cited by in corpus (103)

• Phononic thermal properties of two-dimensional materials
• Hydrodynamic Diffusion in Integrable Systems
• Kardar-Parisi-Zhang physics in the quantum Heisenberg magnet
• Influence of Boundaries and Thermostatting on Nonequilibrium Molecular Dynamics Simulations of Heat Conduction in Solids
• Kardar-Parisi-Zhang universality from soft gauge modes
• Perfect diode in quantum spin chains
• Double scaling in the relaxation time in the $\beta$-FPUT model
• Anomalous heat transport in classical many-body systems: overview and perspectives
• Non-Fourier heat transport in nanosystems
• Fast and slow thermal processes in harmonic scalar lattices
• Optomechanics for thermal characterization of suspended graphene
• Interacting and noninteracting integrable systems
• Anomalous heat transport in one dimensional systems: a description using non-local fractional-type diffusion equation
• Crossover from ballistic to normal heat transport in the ${\varphi }^4$ lattice: If nonconservation of momentum is the reason, what is the mechanism?
• Diffusive Heat Waves in Random Conformal Field Theory
• Role of the range of the interactions in thermal conduction
• Ultrahigh convergent thermal conductivity of carbon nanotubes from comprehensive atomistic modeling
• A violation of universality in anomalous Fourier's law
• Thermal transport in long-range interacting Fermi-Pasta-Ulam chains
• Non-linear fluctuating hydrodynamics for KPZ scaling in isotropic spin chains
• Nonlinear Fluctuating Hydrodynamics for the Classical XXZ Spin Chain
• Discrete breathers assist energy transfer to ac driven nonlinear chains
• Heat current rectification in segmented XXZ chains
• Engineering dynamical couplings for quantum thermodynamic tasks
• Exact confirmation of 1D nonlinear fluctuating hydrodynamics for a two-species exclusion process
• Thermodynamic bound on heat to power conversion
• Wave Turbulence and thermalization in one-dimensional chains
• Phononic heat transport in molecular junctions: quantum effects and vibrational mismatch
• Phononic heat transport in the transient regime: An analytic solution
• Searching for the Tracy-Widom distribution in nonequilibrium processes
• Microscopic theory of the fluctuating hydrodynamics in nonlinear lattices
• Coexistence of ballistic and Fourier regimes in the $\beta$-FPUT lattice
• Transport in perturbed classical integrable systems: the pinned Toda chain
• Equilibrium time-correlation functions of the long-range interacting Fermi-Pasta-Ulam model
• Heat transport in carbon nanotubes: Length dependence of phononic conductivity from the Boltzmann transport equation and molecular dynamics
• Derivation of fluctuating hydrodynamics and crossover from diffusive to anomalous transport in a hard-particle gas
• Harmonic chains and the thermal diode effect
• An efficient thermal diode with ballistic spacer
• Heat transport via a local two-state system near thermal equilibrium
• Heat fluctuations in a harmonic chain of active particles
• Multi-particle collision simulations of 2D one-component plasmas: anomalous transport and dimensional crossovers
• Activity driven transport in harmonic chains
• Coupled transport in rotor models
• Heat transfer in a one-dimensional harmonic crystal in a viscous environment subjected to an external heat supply
• Transport properties of the classical Toda chain: effect of a pinning potential
• Wick polynomials and time-evolution of cumulants
• Reversible thermal diode and energy harvester with a superconducting quantum interference single-electron transistor
• Spatiotemporal Crossover between Low- and High-Temperature Dynamical Regimes in the Quantum Heisenberg Magnet
• Equilibration of sinusoidal modulation of temperature in linear and nonlinear chains
• Heat current fluctuations and anomalous transport in low dimensional carbon lattices
• Diverging fluctuations of the Lyapunov exponents
• Direct Evidence for Universal Statistics of Stationary Kardar-Parisi-Zhang Interfaces
• Pressure-induced recovery of Fourier's law in one dimensional momentum-conserving systems
• Temperature profile and boundary conditions in an anomalous heat transport model
• Kardar-Parisi-Zhang Interfaces with Curved Initial Shapes and Variational Formula
• One-Dimensional Self-Organization and Nonequilibrium Phase Transition in a Hamiltonian System
• Charge-current correlation equalities for quantum systems far from equilibrium
• Shocks, rarefaction waves, and current fluctuations for anharmonic chains
• Dynamics of fluctuation correlation in periodically driven classical system
• One-dimensional Superdiffusive Heat Propagation Induced by Optical Phonon-Phonon Interactions
• Merits and Qualms of Work Fluctuations in Classical Fluctuation Theorems
• Heat conduction in chains of non-locally coupled harmonic oscillators: mean-field limit
• Heat current control in trapped BEC
• Thermalization of two- and three-dimensional classical lattices
• Far-Field Radiative Thermal Rectification with Bulk Materials
• Geometry induced local thermal current from cold to hot in a classical harmonic system
• Blast waves in the zero temperature hard sphere gas: double scaling structure
• Nonlinear Perturbation of a Noisy Hamiltonian Lattice Field Model: Universality Persistence
• Universality in the Onset of Super-Diffusion in Lévy Walks
• Heat conduction in a three-dimensional momentum-conserving fluid
• Quantitative Rates of Convergence to Non-Equilibrium Steady State for a Weakly Anharmonic Chain of Oscillators
• Analytical results for a minimalist thermal diode
• Minimal motor for powering particle motion from spin imbalance
• Universal scaling for recovery of Fourier's law in low-dimensional solids under momentum conservation
• Anomalous temperature-dependent heat transport in one-dimensional momentum-conserving systems with soft-type interparticle interaction
• Nonequilibrium Generalised Langevin Equation for the calculation of heat transport properties in model 1D atomic chains coupled to two 3D thermal baths
• Non-equilibrium steady states of long-range coupled harmonic chains
• A lattice gas model for generic one-dimensional Hamiltonian Systems
• Thermal transport of confined water molecules in quasi-one-dimensional nanotubes
• Heat perturbations spreading in the Fermi-Pasta-Ulam-$\beta$ system with next-nearest-neighbor coupling: Competition between phonon dispersion and nonlinearity
• Conformal order and Poincar$\acute{\mathrm{e}}$-Klein mapping underlying electrostatics-driven inhomogeneity in tethered membranes
• Coupled transport in a linear-stochastic Schrödinger Equation
• Nernst-like Effect in a Flexible Chain
• KPZ modes in $d$-dimensional directed polymers
• Condensation induced by coupled transport processes
• Harmonic chain with velocity flips: thermalization and kinetic theory
• L{é}vy walks on finite intervals: A step beyond asymptotics
• Heat conduction in a chain of colliding particles with stiff repulsive potential
• Correlation Functions for a Chain of Short Range Oscillators
• Heat flux direction controlled by power-law oscillators under non-Gaussian fluctuations
• Equilibrium fluctuation for an anharmonic chain with boundary conditions in the Euler scaling limit
• Existence of a Non-Equilibrium Steady State for the Non-linear BGK equation on an interval
• Mechanisms for transient localization in a diatomic nonlinear chain
• Harmonic chain driven by active Rubin bath: transport properties and steady-state correlations
• Chapman-Enskog theory and crossover between diffusion and superdiffusion for nearly integrable quantum gases
• Negative Differential Heat Conductivity in a Harmonic Chain Coupled to a Particle Reservoir
• Thermalization in asymmetric harmonic chains
• Classical and quantum harmonic mean-field models coupled intensively and extensively with external baths
• Thermal transport in disordered harmonic chains revisited: Formulation of thermal conductivity and local temperatures
• Boundary layers, transport and universal distribution in boundary driven active systems
• Dephasing-assisted macrospin transport
• From Near-Integrable to Far-from-Integrable: A Unified Picture of Thermalization and Heat Transport
• Infinite-temperature thermostats by energy localization in a nonequilibrium setup