Heat Transport in low-dimensional systems

Abstract

Recent results on theoretical studies of heat conduction in low-dimensional systems are presented. These studies are on simple, yet nontrivial, models. Most of these are classical systems, but some quantum-mechanical work is also reported. Much of the work has been on lattice models corresponding to phononic systems, and some on hard particle and hard disc systems. A recently developed approach, using generalized Langevin equations and phonon Green's functions, is explained and several applications to harmonic systems are given. For interacting systems, various analytic approaches based on the Green-Kubo formula are described, and their predictions are compared with the latest results from simulation. These results indicate that for momentum-conserving systems, transport is anomalous in one and two dimensions, and the thermal conductivity kappa, diverges with system size L, as kappa ~ L^alpha. For one dimensional interacting systems there is strong numerical evidence for a universal exponent alpha =1/3, but there is no exact proof for this so far. A brief discussion of some of the experiments on heat conduction in nanowires and nanotubes is also given.

78 pages, 25 figures, Review Article (revised version)

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• Environment dependent vibrational heat transport in molecular Junctions : Rectification, quantum effects, vibrational mismatch
• Exact Solution for the Heat Conductance in Harmonic Chains
• Heat transport in a Coulomb ion crystal with a topological defect
• Heat conduction in a chain of colliding particles with stiff repulsive potential
• Propagation dynamics on the Fermi-Pasta-Ulam lattices
• Eliminating the cuspidal temperature profile of a non-equilibrium chain
• Heat conduction across molecular junctions between nanoparticles
• Non-equilibrium boundary driven quantum systems: models, methods and properties
• Localization properties of harmonic chains with correlated mass and spring disorder: Analytical approach
• Projective-truncation-approximation study of the one-dimensional ${\varphi }^4$ lattice model
• Nonequilibrium Green's functions in the study of heat transport of driven nanomechanical systems
• Influence of vortices and phase fluctuations on thermoelectric transport properties of superconductors in a magnetic field
• Heat flow in anharmonic crystals with internal and external stochastic baths: A convergent polymer expansion for a model with discrete time and long range interparticle interaction
• Heat transport through an open coupled scalar field theory hosting stability-to-instability transition
• Temperature dependent divergence of thermal conductivity in momentum conserving 1D lattice with asymmetric potential
• Thermalization of isolated harmonic networks under conservative noise
• First-principle validation of Fourier's law in d=1,2,3 classical systems
• Cluster sizes in a classical Lennard-Jones chain
• Correlation Functions for a Chain of Short Range Oscillators
• Optimal qubit-mediated quantum heat transfer via noncommuting operators and strong coupling effects
• Unsteady thermal transport in an instantly heated semi-infinite free end Hooke chain
• Quantum noise theory for phonon transport through nanostructures
• Thermal rectification in mass-asymmetric one-dimensional anharmonic oscillator lattices with and without a ballistic spacer
• Thermo-mechanical transport in rotor chains
• Diffusive lossless energy and coherence transfer by noisy coupling
• Non-Equilibrium Steady States in Kac's Model Coupled to a Thermostat
• Non-linear Fluctuating Hydrodynamics with many conserved fields: the case of a 3D anharmonic chain
• Out-of-equilibrium one-dimensional disordered dipole chain
• Autonomous Circular Heat Engine
• Super-diffusion and crossover from diffusive to anomalous transport in a one-dimensional system
• Entropic analysis of the localization-delocalization transition in a one-dimensional correlated lattice
• Harmonic chain driven by active Rubin bath: transport properties and steady-state correlations
• Quantum transport phenomena induced by time-dependent fields
• Heat transport and cooling performance in a nanomechanical system with local and non local interactions
• Transport in boundary-driven quantum spin systems: One-way street for the energy current
• Existence of a Non-Equilibrium Steady State for the Non-linear BGK equation on an interval
• Thermal conductance of suspended nanoribbons: interplay between strain and interatomic potential nonlinearity
• Theory of Applying Heat Flow from Thermostatted Boundary Walls: Dissipative and Local-Equilibrium Responses and Fluctuation Theorems
• A microscopic model of ballistic-diffusive crossover
• Lecture notes on large deviations in non-equilibrium diffusive systems
• Energy diffusion in the long-range interacting spin systems
• Theory of quantum energy transfer in spin chains: From superexchange to ballistic motion
• Thermal expansion in nanoresonators
• Interacting Non-equilibrium Systems with Two Temperatures
• Aspects of the disordered harmonic chain
• Chapman-Enskog theory and crossover between diffusion and superdiffusion for nearly integrable quantum gases
• Thermal transport in long-range interacting harmonic chains perturbed by long-range conservative noise
• Energy current cumulants in one-dimensional systems in equilibrium
• Nanoscale control of heat and spin conductance in artificial spin chains
• Thermal Transport in Phononic Cayley Tree Networks
• Glassy dynamics in disordered oscillator chains
• Local heat current flow in ballistic phonon transport of graphene nanoribbons
• Statistical distribution of bonding distances in a unidimensional solid
• Thermally driven classical Heisenberg model in one dimension with a local time-varying field
• Quantum Repeated Interactions and the Chaos Game
• Low-Temperature Linear Thermal Rectifiers Based on Coriolis forces
• Heat current magnification in Classical and Quantum spin networks
• Approaching the perfect diode limit through a nonlinear interface
• Thermal transport in a 2D stressed nanostructure with mass gradient
• Unusual equilibration of a particle in a potential with a thermal wall
• Heat rectification by two qubits coupled with Dzyaloshinskii-Moriya interaction
• Thermal response of a Fermi-Pasta-Ulam chain with Andersen thermostats
• ELECTRON TRANSPORT AND ELECTRON DENSITY INSIDE ONE-DIMENSIONAL DISORDERED CONDUCTORS: An Analysis of the Electronic-Levels Contribution
• Energy growth for systems of coupled oscillators with partial damping
• Universal thermalization dynamics in (1+1)d QFTs
• Resistor-network anomalies in the heat transport of random harmonic chain
• Crossover dynamics and non-Gaussian fluctuations in inertial active chains
• Nonanomalous heat transport in a one-dimensional composite chain
• Discovery of energy landscapes towards optimized quantum transport: Environmental effects and long-range tunneling
• Stationary state of harmonic chains driven by boundary resetting
• Taxonomy of integrable and ground-state solvable models: Jastrow wave functions on graphs and parent Hamiltonians
• Thermalization and Hydrodynamics of Two-Dimensional Quantum Field Theories
• Neuromorphic heat transport effects in a molecular junction
• Stochastic Thermodynamics of oscillators networks
• Heat transport in a three dimensional slab geometry and the temperature profile of Ingen-Hausz's experiment
• Classical and quantum harmonic mean-field models coupled intensively and extensively with external baths
• Dephasing enhanced transport in boundary-driven quasiperiodic chains
• Thermal transport in disordered harmonic chains revisited: Formulation of thermal conductivity and local temperatures
• Tunable phononic transparency and opacity with isotopic defects
• Heat transport in a two-level system driven by a time-dependent temperature
• Divergent stiffness of one-dimensional growing interfaces
• From Near-Integrable to Far-from-Integrable: A Unified Picture of Thermalization and Heat Transport
• Collisional relaxation and dynamical scaling in multiparticle collisions dynamics
• Weighted average temperature as the effective temperature of a system in contact with two thermal baths
• Unifying renormalized and bare viscosity in two-dimensional molecular dynamics simulations
• Photonic heat transport from weak to strong coupling
• Quantum vs Classical Thermal Transport at Low Temperatures
• Nonlinearity-induced transition in heat conduction through a topological metamaterial of rotors
• Construction of cubic nonlinear lattice free from umklapp processes
• On the Landauer formula in interfacial thermal transport
• Quantum dynamics of a bosonic mode and a two-level system interacting with several reservoirs
• Energy transport in Z3 chiral clock model
• Molecular hints of two-step transition to convective flow via streamline percolation
• Recent progress on thermal transport in one-dimensional long-range interacting Fermi-Pasta-Ulam-Tsingou lattice systems