Thermal conduction in classical low-dimensional lattices

Abstract

Deriving macroscopic phenomenological laws of irreversible thermodynamics from simple microscopic models is one of the tasks of non-equilibrium statistical mechanics. We consider stationary energy transport in crystals with reference to simple mathematical models consisting of coupled oscillators on a lattice. The role of lattice dimensionality on the breakdown of the Fourier's law is discussed and some universal quantitative aspects are emphasized: the divergence of the finite-size thermal conductivity is characterized by universal laws in one and two dimensions. Equilibrium and non-equilibrium molecular dynamics methods are presented along with a critical survey of previous numerical results. Analytical results for the non-equilibrium dynamics can be obtained in the harmonic chain where the role of disorder and localization can be also understood. The traditional kinetic approach, based on the Boltzmann-Peierls equation is also briefly sketched with reference to one-dimensional chains. Simple toy models can be defined in which the conductivity is finite. Anomalous transport in integrable nonlinear systems is briefly discussed. Finally, possible future research themes are outlined.

90 pages, revised version

Cited by in corpus (622)

• Thermal Properties of Graphene, Carbon Nanotubes and Nanostructured Carbon Materials
• Dimensional crossover of thermal transport in few-layer graphene materials
• Phononics: Manipulating heat flow with electronic analogs and beyond
• Thermal diode: Rectification of heat flux
• Heat Transport in low-dimensional systems
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Lévy walks
• Fundamental aspects of steady-state conversion of heat to work at the nanoscale
• Quantum thermal transport in nanostructures
• Third quantization: a general method to solve master equations for quadratic open Fermi systems
• Finite-temperature transport in one-dimensional quantum lattice models
• Interface thermal resistance between dissimilar anharmonic lattice
• A spin-boson thermal rectifier
• Phononic thermal properties of two-dimensional materials
• Current fluctuations in non-equilibrium diffusive systems: an additivity principle
• Role of anharmonic phonon scattering in the spectrally decomposed thermal conductance at planar interfaces
• Phonon Transport in Graphene
• Nonlinear fluctuating hydrodynamics for anharmonic chains
• Thermal and Thermoelectric Properties of Graphene
• Asymmetric Properties of Heat Conduction in a One-Dimensional Frenkel-Kontorova Model
• Diffusive and subdiffusive spin transport in the ergodic phase of a many-body localizable system
• Anomalous Size Dependence of the Thermal Conductivity of Graphene Ribbons
• Heat dissipation in atomic-scale junctions
• Frequency-dependent phonon mean free path in carbon nanotubes from non-equilibrium molecular dynamics
• Thermal rectification and negative differential thermal resistance in lattices with mass gradient
• Thermal Conductivity of Suspended Graphene with Defects
• Thermal rectification in carbon nanotube intramolecular junctions: Molecular dynamics calculations
• Nonequilibrium Green's function approach to mesoscopic thermal transport
• Influence of Boundaries and Thermostatting on Nonequilibrium Molecular Dynamics Simulations of Heat Conduction in Solids
• Modeling heat transport through completely positive maps
• A momentum conserving model with anomalous thermal conductivity in low dimension
• Heat transport in harmonic lattices
• Thermal conductivity decomposition in two-dimensional materials: Application to graphene
• Chirality- and thickness-dependent thermal conductivity of few-layer graphene: a molecular dynamics study
• Fourier's Law for a Harmonic Crystal with Self-consistent Stochastic Reservoirs
• Thermal conduction of carbon nanotubes using molecular dynamics
• Divergence of the Thermal Conductivity in Uniaxially Strained Graphene
• Heat flow in nonlinear molecular junctions
• Carbon Nanotube Thermal Transport: Ballistic to Diffusive
• Anomalous Heat Diffusion
• Anomalous Heat Diffusion
• Current fluctuations in the one dimensional Symmetric Exclusion Process with open boundaries
• Local Temperature and Universal Heat Conduction in FPU chains
• From anomalous energy diffusion to Levy walks and heat conductivity in one-dimensional systems
• Vibrational Heat Transport in Molecular Junctions
• Dynamic Correlators of Fermi-Pasta-Ulam Chains and Nonlinear Fluctuating Hydrodynamics
• Highly Anistoropic Thermal Conductivity of Arsenene: An ab initio Study
• Nonlinear supratransmission and bistability in the Fermi-Pasta-Ulam model
• Intriguing Heat Conduction of a Polymer Chain
• Phononic Frequency Combs via Nonlinear Resonances
• Anomalous Heat Conduction and Anomalous Diffusion in Low Dimensional Nanoscale Systems
• Fermi-Pasta-Ulam $\beta$ lattice: Peierls equation and anomalous heat conductivity
• Charge and spin transport in strongly correlated one-dimensional quantum systems driven far from equilibrium
• Quantum thermal transport from classical molecular dynamics
• Numerical test of hydrodynamic fluctuation theory in the Fermi-Pasta-Ulam chain
• Transport in Almost Integrable Models: Perturbed Heisenberg Chains
• Layer and size dependence of thermal conductivity in multilayer graphene nanoribbons
• Cumulants and large deviations of the current through non-equilibrium steady states
• Controlling and measuring quantum transport of heat in trapped-ion crystals
• The phonon Boltzmann equation, properties and link to weakly anharmonic lattice dynamics
• Nonequilibrium Green's function method for thermal transport in junctions
• Heat transport through lattices of quantum harmonic oscillators in arbitrary dimensions
• Anomalous heat conduction and anomalous diffusion in nonlinear lattices, single walled nanotubes, and billiard gas channels
• Fourier's Law from Schroedinger Dynamics
• Nonequilibrium Green's function method for phonon-phonon interaction and ballistic-diffusive thermal transport
• Dynamical heat channels
• Generalized Bose-Einstein condensation into multiple states in driven-dissipative systems
• On the universality of anomalous one-dimensional heat conductivity
• Self-Consistent Mode-Coupling Approach to 1D Heat Transport
• Symmetries in Fluctuations Far from Equilibrium
• Equivalence of the equilibrium and the nonequilibrium molecular dynamics methods for thermal conductivity calculations: From bulk to nanowire silicon
• Microscopic versus macroscopic approaches to non-equilibrium systems
• Many-body Green's function approach to lattice thermal transport
• Heat transport and phonon localization in mass-disordered harmonic crystals
• Heat conduction in a three dimensional anharmonic crystal
• Normal heat conduction in one dimensional momentum conserving lattices with asymmetric interactions
• Compactons and Chaos in Strongly Nonlinear Lattices
• Coupled electron and phonon transport in one-dimensional atomic junctions
• Thermal Conductivity of Spin-1/2 Chains
• Heat conduction in the α-β-Fermi-Pasta-Ulam chain
• Thermal Conductivity for a Momentum Conserving Model
• Energy carriers in the Fermi-Pasta-Ulam $\beta$ lattice: Solitons or Phonons?
• Ratcheting Heat Flux against a Thermal Bias
• Test of the Additivity Principle for Current Fluctuations in a Model of Heat Conduction
• Energy Transport in Weakly Anharmonic Chains
• Fermi-Pasta-Ulam model with long-range interactions: Dynamics and thermostatistics
• Origin of negative differential thermal resistance in a chain of two weakly coupled nonlinear lattices
• Dynamical Thermalization of Disordered Nonlinear Lattices
• Nonlinear Fluctuating Hydrodynamics in One Dimension: the Case of Two Conserved Fields
• Energy transport between two integrable spin chains
• Anomalous kinetics and transport from 1D self--consistent mode--coupling theory
• Kondo signature in heat transfer via a local two-state system
• Studies of thermal conductivity in Fermi-Pasta-Ulam like lattices
• Transport in open spin chains: A Monte Carlo wave-function approach
• Fourier's Law in a Quantum Spin Chain and the Onset of Quantum Chaos
• Graded anharmonic crystals as genuine thermal diodes: Analytical description of rectification and negative differential thermal resistance
• Limit theorems for additive functionals of a Markov chain
• Validity of Fourier's law in one-dimensional momentum-conserving lattices with asymmetric interparticle interactions
• High temperature thermal conductivity of 2-leg spin-1/2 ladders
• Mode-coupling theory and molecular dynamics simulation for heat conduction in a chain with transverse motions
• A generalized Debye-Peierls/Allen-Feldman model for the lattice thermal conductivity of low dimensional and disordered materials
• Density dynamics in translationally invariant spin-1/2 chains at high temperatures: a current auto-correlation approach to finite time- and length-scales
• Exact solution of a Levy walk model for anomalous heat transport
• Nonequilibrium Energy Profiles for a Class of 1-D Models
• Magnetically Induced Thermal Rectification
• Negative differential conductivity in far-from-equilibrium quantum spin chains
• High-temperature coherent transport in the XXZ chain in the presence of an impurity
• Non-integrability and the Fourier heat conduction law
• Nonlinear quantum heat transfer in hybrid structures: Sufficient conditions for thermal rectification
• Too Close to Integrable: Crossover from Normal to Anomalous Heat Diffusion
• Superdiffusion of energy in a chain of harmonic oscillators with noise
• Anomalous energy transport in the FPU-beta chain
• Nonlinear Waves in Disordered Diatomic Granular Chains
• Universality classes of spin transport in one-dimensional isotropic magnets: the onset of logarithmic anomalies
• Energy transport in stochastically perturbed lattice dynamics
• Optomechanical measurement of thermal transport in two-dimensional MoSe2 lattices
• Shuttling heat across 1D homogenous nonlinear lattices with a Brownian heat motor
• A stochastic model of anomalous heat transport: analytical solution of the steady state
• The nonequilibrium discrete nonlinear Schroedinger equation
• Generalization of Fourier's law into viscous heat equations
• Electron transport in a one dimensional conductor with inelastic scattering by self-consistent reservoirs
• Entropy of Open Lattice Systems
• Phonon Engineering of the Specific Heat of Twisted Bilayer Graphene: The Role of the Out-of-Plane Phonon Modes
• Non-equilibrium stationary state of a harmonic crystal with alternating masses
• Macroscopic Diffusive Transport in a Microscopically Integrable Hamiltonian System
• Statistical Mechanics of Systems with Negative Temperature
• Effective phonons in anharmonic lattices: anomalous vs normal heat conduction
• Quantum heat transfer in harmonic chains with self consistent reservoirs: Exact numerical simulations
• Designing a Spin-Seebeck Diode
• Thermal rectifier from deformed carbon nanohorns
• On the propagation of binary signals in damped mechanical systems of oscillators
• Diffusion of heat, energy, momentum, and mass in one-dimensional systems
• Current fluctuations for anharmonic chains in thermal equilibrium
• Anomalous heat transport in classical many-body systems: overview and perspectives
• Non-Fourier heat transport in nanosystems
• Current Fluctuations and Statistics During a Large Deviation Event in an Exactly-Solvable Transport Model
• Equilibrium time-correlation functions for one-dimensional hard-point systems
• Generating Function Formula of Heat Transfer in Harmonic Networks
• Fast and slow thermal processes in harmonic scalar lattices
• The effect of discrete breathers on heat conduction in nonlinear chains
• Fluctuating hydrodynamics for a discrete Gross-Pitaevskii equation: mapping to Kardar-Parisi-Zhang universality class
• Thermal Rectification in Billiard-like Systems
• Normal Heat Conduction in a Chain with Weak Interparticle Anharmonic Potential
• The adjustable thermal resistor by reversibly folding a graphene sheet
• Heat flux operator, current conservation and the formal Fourier's law
• Length dependence of the thermal conductance of alkane-based single-molecule junctions: An ab-initio study
• Maximization and Minimization of Interfacial Thermal Conductance by Modulating the Mass Distribution of Interlayer
• Supersonic Discrete Kink-Solitons and Sinusoidal Patterns with "Magic" wavenumber in Anharmonic Lattices
• Universality of One-Dimensional Heat Conductivity
• Time evolution of the Luttinger model with nonuniform temperature profile
• Transport in a one-dimensional isotropic Heisenberg model at high temperature
• Anomalous heat transport in one dimensional systems: a description using non-local fractional-type diffusion equation
• Heat transport in oscillator chains with long-range interactions coupled to thermal reservoirs
• Counting statistics of heat transport in harmonic junctions -- transient and steady states
• Non-equilibrium Statistical Mechanics of Anharmonic Crystals with Self-consistent Stochastic Reservoirs
• Nonlinear lattice waves in heterogeneous media
• Thermal rectification in quantum graded mass systems
• Designing nonlinear thermal devices and metamaterials under the Fourier's law: A route to nonlinear thermotics
• Thermal transport in the Fermi-Pasta-Ulam model with long-range interactions
• 1D momentum-conserving systems: the conundrum of anomalous versus normal heat transport
• Energy diffusion in hard-point systems
• Coupled Kardar-Parisi-Zhang Equations in One Dimension
• Thermal conductivity of anharmonic lattices: Effective phonons and quantum corrections
• Thermal balance and quantum heat transport in nanostructures thermalized by local Langevin heat baths
• Density Profiles in Open Superdiffusive Systems
• Crossover from ballistic to diffusive thermal transport in quantum Langevin dynamics study of a harmonic chain connected to self-consistent reservoirs
• Crossover from ballistic to normal heat transport in the ${\varphi }^4$ lattice: If nonconservation of momentum is the reason, what is the mechanism?
• Steady state thermal transport in anharmonic systems: Application to molecular junctions
• Green-Kubo formula for heat conduction in open systems
• Weak and strong chaos in FPU models and beyond
• Brownian motion and diffusion: from stochastic processes to chaos and beyond
• Thermal transport in out of equilibrium quantum harmonic chains
• Negative differential thermal resistance induced by ballistic transport
• Quantum effects in thermal conduction: Nonequilibrium quantum discord and entanglement
• Large Fluctuations of the Macroscopic Current in Diffusive Systems: A Confirmation of the Additivity Principle
• Anomalous diffusion for a class of systems with two conserved quantities
• Role of the range of the interactions in thermal conduction
• Energy Rectification in Quantum Graded Spin Chains: Analysis of the XXZ Model
• Heat conductivity of DNA double helix
• Heat flow in chains driven by thermal noise
• Superdiffusive Transport and Energy Localization in Disordered Granular Crystals
• Nonlinear Lattice Dynamics of Bose-Einstein Condensates
• Nonlinear driven diffusive systems with dissipation: fluctuating hydrodynamics
• Ultrahigh convergent thermal conductivity of carbon nanotubes from comprehensive atomistic modeling
• 3/4 Fractional superdiffusion of energy in a system of harmonic oscillators perturbed by a conservative noise
• Limited validity of the Kubo formula for thermal conduction in modular quantum systems
• Density dynamics from current auto-correlations at finite time- and length-scales
• Steady states and universal conductance in a quenched Luttinger model
• Transmission thresholds in time-periodically driven nonlinear disordered systems
• A violation of universality in anomalous Fourier's law
• Geometric Heat Flux for Classical Thermal Transport in Interacting Open Systems
• Arbitrarily Weak Nonlinearity Can Destroy the Anderson Localization
• Non-equilibrium steady states of ideal bosonic and fermionic quantum gases
• Normal Heat Conductivity in a strongly pinned chain of anharmonic oscillators
• Energy distribution and local fluctuations in strongly coupled open quantum systems: The extended resonant level model
• Generalized kinetic and evolution equations in the approach of the nonequilibrium statistical operator
• Equilibrium dynamical correlations in the Toda chain and other integrable models
• Bound particle coupled to two thermostats
• Off-equilibrium Langevin dynamics of the discrete nonlinear Schroedinger chain
• Twist-Dependent Anisotropic Thermal Conductivity in Homogeneous MoS${}_2$ Stacks
• ThermoElectric Transport Properties of a Chain of Quantum Dots with Self-Consistent Reservoirs
• Thermal transport in long-range interacting Fermi-Pasta-Ulam chains
• Temperature Profiles in Hamiltonian Heat Conduction
• Discrete breathers assist energy transfer to ac driven nonlinear chains
• Nonequilibrium Steady State in Open Quantum Systems: Influence Action, Stochastic Equation and Power Balance
• Fourier law from a chain of coupled anharmonic oscillators under energy conserving noise
• Role of pinning potentials in heat transport through disordered harmonic chain
• Heat Transport in Quantum Spin Chains: Stochastic Baths vs Quantum Trajectories
• Breakdown of Hydrodynamics in a Simple One-Dimensional Fluid
• Heat conduction in deformable Frenkel-Kontorova lattices: thermal conductivity and negative differential thermal resistance
• Heat Conduction in One-Dimensional chain of Hard Discs with Substrate Potential
• Heat conduction in the disordered Fermi-Pasta-Ulam chain
• Non-diffusive Lattice Thermal Transport in Si-Ge Alloy Nanowires
• Nonequilibrium dynamics of a stochastic model of anomalous heat transport
• Detailed Examination of Transport Coefficients in Cubic-Plus-Quartic Oscillator Chains
• Heat, Work and Energy Currents in the Boundary-Driven XXZ Spin Chain
• Heat Conduction in two-dimensional harmonic crystal with disorder
• Fourier's Law from Closure Equations
• A microscopic mechanism for increasing thermoelectric efficiency
• Negative thermal conductivity of chains of rotors with mechanical forcing
• Crossover from Fermi-Pasta-Ulam to normal diffusive behaviour in heat conduction through open anharmonic lattices
• Thermalization in Open Quantum Systems
• Graphene Helicoid: The Distinct Properties Promote Application of Graphene Related Materials in Thermal Management
• Conservation Laws and Thermodynamic Efficiencies
• Non-stationary heat conduction in one-dimensional chains with conserved momentum
• Density-Functional Theory of Thermoelectric Phenomena
• Exact confirmation of 1D nonlinear fluctuating hydrodynamics for a two-species exclusion process
• Ballistic resonance and thermalization in Fermi-Pasta-Ulam-Tsingou chain at finite temperature
• Ingredients for an efficient thermal diode
• Tuning heat transport in trapped-ion chains across a structural phase transition
• Effects of breaking vibrational energy equipartition on measurements of temperature in macroscopic oscillators subject to heat flux
• Quantum Mechanical Heat Transport in Disordered Harmonic Chains
• Supersolitons: Solitonic excitations in atomic soliton chains
• Triggering waves in nonlinear lattices: Quest for anharmonic phonons and corresponding mean free paths
• Microscopic Quantum Mechanical Foundation of Fourier's Law
• Universality classes in two-component driven diffusive systems
• Normal Transport Behavior in Finite One-Dimensional Chaotic Quantum Systems
• Thermal conductivity of one-, two- and three-dimensional carbon
• Energy current correlation in solvable long-range interacting systems
• Double negative differential thermal resistance induced by the nonlinear on-site potentials
• Hyperbolic heat conduction, effective temperature and third law in the presence of heat flux
• Thermodynamic bound on heat to power conversion
• Fourier law in a momentum-conserving chain
• Crossover behavior of the thermal conductance and Kramers' transition rate theory
• Wave Turbulence and thermalization in one-dimensional chains
• A Chain, a Bath, a Sink and a Wall
• Nonequilibrium steady-state Kubo formula: equality of transport coefficients
• Scaling analysis of negative differential thermal resistance
• How can we derive Fourier's Law from quantum mechanics? Exact master equation analysis
• Ballistic transport and boundary resistances in inhomogeneous quantum spin chains
• Molecular dynamics with quantum heat baths: results for nanoribbons and nanotubes
• Phononic heat transport in the transient regime: An analytic solution
• Fourier's law from a chain of coupled planar harmonic oscillators under energy conserving noise
• Heat transport via low-dimensional systems with broken time-reversal symmetry
• Anomalous Heat Conduction in Three-Dimensional Nonlinear Lattices
• Phononic heat transport in molecular junctions: quantum effects and vibrational mismatch
• Key role of asymmetric interactions in low-dimensional heat transport
• All-phononic Digital Transistor on the Basis of Gap-Soliton Dynamics in Anharmonic Oscillator Ladder
• Finite-size effects on current correlation functions
• Rectification of heat currents across nonlinear quantum chains: A versatile approach beyond weak thermal contact
• Microscopic theory of the fluctuating hydrodynamics in nonlinear lattices
• Normal heat conductivity in chains capable of dissociation
• Anomalous fluctuations for a perturbed Hamiltonian system with exponential interactions
• From thermal rectifiers to thermoelectric devices
• Thermal conductivities of one-dimensional anharmonic/nonlinear lattices: renormalized phonons and effective phonon theory
• Non-equilibrium steady states for chains of four rotors
• Coexistence of ballistic and Fourier regimes in the $\beta$-FPUT lattice
• Transport in perturbed classical integrable systems: the pinned Toda chain
• 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
• The one-dimensional Lennard-Jones system: collective fluctuations and breakdown of hydrodynamics
• Equilibrium time-correlation functions of the long-range interacting Fermi-Pasta-Ulam model
• Nonequilibrium dynamics of a stochastic model of anomalous heat transport: numerical analysis
• The Fourier heat conduction as a strong kinetic effect
• Thermoelectric efficiency in momentum-conserving systems
• An efficient thermal diode with ballistic spacer
• Stretched--exponential relaxation in arrays of coupled rotators
• Solving Optimization Problems through Fully Convolutional Networks: an Application to the Travelling Salesman Problem
• Dimension dependence of negative differential thermal resistance in graphene nanoribbons
• Nonequilibrium Invariant Measure under Heat Flow
• Heat conduction in 2D strongly-coupled dusty plasmas
• Activity driven transport in harmonic chains
• Strong system-bath coupling induces negative differential thermal conductance and heat amplification in nonequilibrium two-qubits systems
• Heat fluctuations in a harmonic chain of active particles
• Quantum heat transfer: A Born Oppenheimer method
• Fractional diffusion equation description of an open anomalous heat conduction set-up
• Multi-particle collision simulations of 2D one-component plasmas: anomalous transport and dimensional crossovers
• Coupled transport in rotor models
• Discrete solitons in self-defocusing systems with $\mathcal{P}\mathcal{T}$-symmetric defects
• Heat transfer in a one-dimensional harmonic crystal in a viscous environment subjected to an external heat supply
• Renormalized phonons in nonlinear lattices: A variational approach
• Thermal conductivity of the Toda lattice with conservative noise
• Equivalence of transport coefficients in bath-induced and dynamical scenarios
• Rectification and One-Way Street for the Energy Current in Boundary-Driven Asymmetric Quantum Spin Chains
• Transport Control in Low-Dimensional Spin-1/2 Heisenberg Systems
• Displacement Autocorrelation Functions for Strong Anomalous Diffusion: A Scaling Form, Universal Behavior, and Corrections to Scaling
• Localization of low-frequency oscillations in single-walled carbon nanotubes
• Macroscopic energy diffusion for a chain of anharmonic oscillators
• Unsteady ballistic heat transport in infinite harmonic crystals
• Thermo-magnonic diode: rectification of energy and magnetization currents
• Anisotropic In-Plane Phonon Transport in Ultrathin Silicon Membranes Guided by Nano-Surface-Resonators
• Interfacial thermal transport with strong system-bath coupling: A phonon delocalization effect
• Crossover between different universality classes: Scaling for thermal transport in one dimension
• Fourier's law based on microscopic dynamics
• A Rich Example of Geometrically Induced Nonlinearity: From Rotobreathers and Kinks to Moving Localized Modes and Resonant Energy Transfer
• About thermometers and temperature
• Transport through interacting defects and lack of thermalisation
• Energy repartition for a harmonic chain with local reservoirs
• High-frequency thermal processes in harmonic crystals
• Modulational instability in isolated and driven Fermi--Pasta--Ulam lattices
• Transport properties of the classical Toda chain: effect of a pinning potential
• From normal diffusion to superdiffusion of energy in the evanescent flip noise limit
• Transport properties in chaotic and non-chaotic many particles systems
• Nonstationary heat conduction in one-dimensional models with substrate potential
• Nonequilibrium phonon mean free paths in anharmonic chains
• Collective excitations of dipolar gases based on local tunneling in superlattices
• Long-range steady state density profiles induced by localized drive
• Bath assisted transport in a three-site spin chain: global {\sl vs} local approach
• Thermal conduction and interface effects in nanoscale Fermi-Pasta-Ulam conductors
• The role of the nature of the noise in the thermal conductance of mechanical systems
• Steady-state kinetic temperature distribution in a two-dimensional square harmonic scalar lattice lying in a viscous environment and subjected to a point heat source
• Exact Shannon entropies for the multidimensional harmonic states
• A unified theory of second sound in two dimensional materials
• Transport of quantum excitations coupled to spatially extended nonlinear many-body systems
• Memory Effects in Nonequilibrium Transport for Deterministic Hamiltonian Systems
• Anomalous dynamical scaling in anharmonic chains and plasma models with multiparticle collisions
• Heisenberg and entropic uncertainty measures for large-dimensional harmonic systems
• Ballistic and superdiffusive scales in macroscopic evolution of a chain of oscillators
• Nonlinear thermal control in an N-terminal junction
• Understanding Divergent Thermal Conductivity in Single Polythiophene Chains using Modal Analysis and Sonification
• Temperature dependence of thermal conductivities of coupled rotator lattice and the momentum diffusion in standard map
• Boundary-induced instabilities in coupled oscillators
• Asymptotic energy profile of a wavepacket in disordered chains
• Thermal conductivity of a classical one dimensional spin-phonon system
• Anomalies, absence of local equilibrium and universality in 1-d particles systems
• Equilibration of sinusoidal modulation of temperature in linear and nonlinear chains
• A general fluctuation-response relation for noise variations and its application to driven hydrodynamic experiments
• A Billiard-Theoretic Approach to Elementary 1d Elastic Collisions
• A simulation study of energy transport in the Hamiltonian XY-model
• Additivity Principle in High-dimensional Deterministic Systems
• A perturbative approach for the crystal chains with self-consistent stochastic reservoirs
• Fluctuations of the heat flux of a one-dimensional hard particle gas
• Current fluctuations at a phase transition
• Temperature profile and boundary conditions in an anomalous heat transport model
• Anomalous negative differential thermal resistance in a momentum-conserving lattice
• Defining the effective temperature of a quantum driven system from current-current correlation functions
• Preferential Sampling of Elastic Chains in Turbulent Flows
• Pressure-induced recovery of Fourier's law in one dimensional momentum-conserving systems
• Exact time-averaged thermal conductance for small systems: Comparison between direct calculation and Green-Kubo formalism
• Drastic fall-off of the thermal conductivity for disordered lattices in the limit of weak anharmonic interactions
• Proposal for a single-molecule field-effect transistor for phonons
• Anomalous energy diffusion in two-dimensional nonlinear lattices
• Heat flux in one-dimensional systems
• Thermoelectricity of interacting particles: A numerical approach
• Thermal Rectification in Classical and Quantum Systems: Searching for Efficient Thermal Diodes
• Heat wave propagation in a nonlinear chain
• Underlying mechanisms for normal heat transport in one-dimensional anharmonic oscillator systems with a double-well interparticle interaction
• Different thermal conductance of the inter- and intra-chain interactions in a double-stranded molecular structure
• Thermal conductivity for coupled charged harmonic oscillators with noise in a magnetic field
• One-Dimensional Self-Organization and Nonequilibrium Phase Transition in a Hamiltonian System
• Thermal conductance of the Fermi-Pasta-Ulam chains: Atomic to mesoscopic transition
• Thermal echo in a finite one-dimensional harmonic crystal
• Local rectification of heat flux
• Thermal Conductivity for a Noisy Disordered Harmonic Chain
• Thermal rectification in the thermodynamic limit
• Anomalous energy transport in FPU-$\beta$ chain
• Asymmetric Heat Transport in Ion Crystals
• Transport, correlations, and chaos in a classical disordered anharmonic chain
• Thermal conductivity of the degenerate one-dimensional Fermi gas
• Interaction of phonons with discrete breather in strained graphene
• Heat transport in long-ranged anharmonic oscillator models
• Anomalous thermal properties of a harmonic chain with correlated isotopic disorder
• Invariance principle for wave propagation inside inhomogeneously disordered materials
• Unsteady ballistic heat transport in a 1D harmonic crystal due to a source on an isotopic defect
• The Simplest Piston Problem I: Elastic Collisions
• Temperature response in nonequilibrium stochastic systems
• Heat conduction and energy diffusion in momentum-conserving 1D full lattice ding-a-ling model
• Quantum transport in chains with noisy off-diagonal couplings
• Observing Golden Mean Universality Class in the Scaling of Thermal Transport
• Numerical examination of steady-state thermodynamics from the entropy connected to the excess heat
• Energy spread and current-current correlation in quantum systems
• Thermal conduction in molecular chains: Non-Markovian effects
• Heat current control in trapped BEC
• Modulating heat conduction by stretching or compressing
• Enhancement and reduction of one-dimensional heat conduction with correlated mass disorder
• Entropy production and heat transport in harmonic chains under time dependent periodic drivings
• Thermal response in driven diffusive systems
• Anomalous Fourier's law and long range correlations in a 1D non-momentum conserving mechanical model
• Nonequilibrium thermomechanics of Gaussian phase packet crystals: application to the quasistatic quasicontinuum method
• Heat conduction in chains of non-locally coupled harmonic oscillators: mean-field limit
• Normal heat conductivity in two-dimensional scalar lattices
• Exact steady state of the open XX-spin chain: entanglement and transport properties
• One-dimensional Superdiffusive Heat Propagation Induced by Optical Phonon-Phonon Interactions
• A one dimensional hard-point gas as a thermoelectric engine
• Steady-state ballistic thermal transport associated with transversal motions in a damped graphene lattice subjected to a point heat source
• From a kinetic equation to a diffusion under an anomalous scaling
• Dynamics and transport in the boundary-driven dissipative Klein-Gordon chain
• The thermoelectric working fluid: thermodynamics and transport
• Using Hilbert transform and classical chains to simulate quantum walks
• Diffusive Propagation of Energy in a Non-Acoustic Chain
• Quantum nanofriction in trapped ion chains with a topological defect
• Hamiltonian model of heat conductivity and Fourier law
• Interfacial thermal conduction and negative temperature jump in one-dimensional lattices
• Temperature-dependent thermal conductivities of one-dimensional nonlinear Klein-Gordon lattices with soft on-site potential
• Thermoelectricity of cold ions in optical lattices
• Nonequilibrium statistical mechanics of weakly stochastically perturbed system of oscillators
• Change of entropy for the one-dimensional ballistic heat equation: Sinusoidal initial perturbation
• Thermalization of two- and three-dimensional classical lattices
• Coherent energy transport in classical nonlinear oscillators: an analogy with the Josephson effect
• Beyond the Lindblad Master Equation: Heat, Work and Energy Currents in Boundary Driven Spin Chains
• Energy Diffusion in Harmonic System with Conservative Noise
• Phonon Scattering at Kinks in Suspended Graphene
• Heat generation and transport due to time-dependent forces
• Existence of negative differential thermal conductance in one-dimensional diffusive thermal transport
• Vibrational model of heat transfer in strongly coupled Yukawa fluids (dusty plasma liquids)
• Heat conduction in a confined solid strip: Response to external strain
• Energy Dissipation in Hamiltonian Chains of Rotators
• Thermal conductivity of nonlinear waves in disordered chains
• The Role of Chaos in One-Dimensional Heat Conductivity
• Thermal conduction in two-dimensional complex plasma layers
• Dynamic Screening in a Two-Species Asymmetric Exclusion Process
• Rectification of energy and motion in non-equilibrium parity violating metamaterials
• Classical Heat Transport in Anharmonic Molecular Junctions: Exact Solutions
• Nonequilibrium Steady States for Certain Hamiltonian Models
• Heat transport in nonlinear lattices free from the Umklapp process
• Thermal conductance of one dimensional disordered harmonic chains
• Superdiffusive Heat Transport in a class of Deterministic One-Dimensional Many-Particle Lorentz gases
• Quantum Transport of Energy in Controlled Synthetic Quantum Magnets
• Asymmetric fluctuation-relaxation paths in FPU models
• Geometry induced local thermal current from cold to hot in a classical harmonic system
• Scaling Theory of Heat Transport in Quasi-1D Disordered Harmonic Chains
• Normal heat conduction in lattice models with asymmetry harmonic interparticle interactions
• Blast waves in the zero temperature hard sphere gas: double scaling structure
• Configurations and Observables in an Ising Model with Heat Flow
• Macroscopically measurable force induced by temperature discontinuities at solid-gas interfaces
• Solitons as candidates for energy carriers in Fermi-Pasta-Ulam lattices
• Kinetic and hydrodynamic regimes in multi-particle-collision dynamics of a one-dimensional fluid with thermal walls
• Controllability for chains of dynamical scatterers
• Thermal conductance of the coupled-rotator chain: Influence of temperature and size
• Effective microscopic models for sympathetic cooling of atomic gases
• Wigner crystal diode
• Thermoelectricity of Wigner crystal in a periodic potential
• Analytical results for a minimalist thermal diode
• Existence of exponentially spatially localised breather solutions for lattices of nonlinearly coupled particles: Schauder's fixed point theorem approach
• Heat conduction in a three-dimensional momentum-conserving fluid
• Out-of-equilibrium Frenkel-Kontorova model
• Quantitative Rates of Convergence to Non-Equilibrium Steady State for a Weakly Anharmonic Chain of Oscillators
• Concentration-of-measure theory for structures and fluctuations of waves
• Hydrodynamics of granular particles on a line
• Entropy production for complex Langevin equations
• Currents and fluctuations of quantum heat transport in harmonic chains
• Nonequilibrium Generalised Langevin Equation for the calculation of heat transport properties in model 1D atomic chains coupled to two 3D thermal baths
• Anomalous temperature-dependent heat transport in one-dimensional momentum-conserving systems with soft-type interparticle interaction
• Step Heat Profile in Localized Chains
• Universal scaling for recovery of Fourier's law in low-dimensional solids under momentum conservation
• Stable and unstable periodic orbits in the one dimensional lattice ${\varphi }^4$ theory
• Ehrenfest approach to open double-well dynamics
• On the limiting Markov process of energy exchanges in a rarely interacting ball-piston gas
• Stretch diffusion and heat conduction in 1D nonlinear lattices
• Probing local equilibrium in nonequilibrium fluids
• Conductivity in the Heisenberg chain with next to nearest neighbor interaction
• Thermally driven classical Heisenberg model in one dimension
• Monte Carlo simulation of size-effects on thermal conductivity in a 2-dimensional Ising system
• Linear response formula for finite frequency thermal conductance of open systems
• Thermal conductivity of one-dimensional lattices with self-consistent heat baths: a heuristic derivation
• Divergent Thermal Conductivity in Three-dimensional Nonlinear lattices
• Thermal transport of confined water molecules in quasi-one-dimensional nanotubes
• Nonequilibrium Steady State and Heat Transport in Nonlinear Open Quantum Systems: Stochastic Influence Action and Functional Perturbative Analysis
• Energy localization in interacting atomic chains with topological solitons
• Random Matrix Theory approach to Mesoscopic Fluctuations of Heat Current
• Dissipation and Entropy Production in Deterministic Heat Conduction of Quasi-one-dimensional Systems
• Microscopic energy flows in disordered Ising spin systems
• Heat transport along a chain of coupled quantum harmonic oscillators
• Variational approach to renormalized phonon in momentum-nonconserving nonlinear lattices
• Conformal order and Poincar$\acute{\mathrm{e}}$-Klein mapping underlying electrostatics-driven inhomogeneity in tethered membranes
• Heat perturbations spreading in the Fermi-Pasta-Ulam-$\beta$ system with next-nearest-neighbor coupling: Competition between phonon dispersion and nonlinearity
• Asymptotics of the solutions of the stochastic lattice wave equation
• Non-equilibrium steady states of long-range coupled harmonic chains
• Hydrodynamics and transport in the long-range-interacting ${\phi }^4$ chain
• Nonequilibrium phenomena in nonlinear lattices: from slow relaxation to anomalous transport
• Energy Transport in Closed Quantum Systems
• Analytic calculation of energy transfer and heat flux in a one-dimensional system
• Kapitza resistance in basic chain models with isolated defects
• Ballistic Heat Conduction and Mass Disorder in One Dimension
• From deterministic dynamics to kinetic phenomena
• Time auto-correlation function and Green-Kubo formula: A study on disordered harmonic chain
• Thermal Rectification and Negative Differential Thermal Resistance in a driven two segment classical Heisenberg chain
• Energy Transport in an Ising Disordered Model
• On the Asymptotic Behavior of the Kernel Function in the Generalized Langevin Equation: A One-dimensional lattice model
• Strong Shock Waves and Nonequilibrium Response in a One-dimensional Gas: a Boltzmann Equation Approach
• Long range correlations in stochastic transport with energy and momentum conservation
• Negative-temperature Fourier transport in one-dimensional systems
• Nernst-like Effect in a Flexible Chain
• Spectrally Sharp Near-Field Thermal Emission: Revealing Some Disagreements between a Casimir-Polder Sensor and Predictions from Far-Field Emittance
• Condensation induced by coupled transport processes
• Long-Time Behavior of Velocity Autocorrelation Function for Interacting Particles in a Two-Dimensional Disordered System
• Heat conduction in a chain of dissociating particles: effect of dimensionality
• Thermalization of oscillator chains with onsite anharmonicity and comparison with kinetic theory
• Thermal Conduction in one dimensional ${\Phi }^4$ chains with colliding particles
• Coupled transport in a linear-stochastic Schrödinger Equation
• Fourier's Law in a Generalized Piston Model
• Linear response of hydrodynamically-coupled particles under a nonequilibrium reservoir
• Delocalization and heat transport in multidimensional trapped ion systems
• Backward and covariant Lyapunov vectors and exponents for hard disk systems with a steady heat current
• Scaling laws and bulk-boundary decoupling in heat flow
• On two reversible cellular automata with two particle species
• Simple analytical model of a thermal diode
• Anomalous interfacial temperature profile induced by phonon localization
• On the local space-time structure of non-equilibrium steady states
• Gauge invariance and geometric phase in nonequilibrium thermodynamics
• Heat transport in a Coulomb ion crystal with a topological defect
• Non-stationary elastic wave scattering and energy transport in a one-dimensional harmonic chain with an isotopic defect
• A Unified Interface Model for Dissipative Transport of Bosons and Fermions
• Hysteresis of noninteracting and spin-orbit coupled atomic Fermi gases with relaxation
• Propagation dynamics on the Fermi-Pasta-Ulam lattices
• Heat conduction in a chain of colliding particles with stiff repulsive potential
• Anomalous long-range correlations at a non-equilibrium phase transition
• Long time, large scale limit of the Wigner transform for a system of linear oscillators in one dimension
• Quantum compacton vacuum
• 5/6-Superdiffusion of energy for coupled charged harmonic oscillators in a magnetic field
• Generalized second fluctuation-dissipation theorem in the nonequilibrium steady state: Theory and applications
• Environment dependent vibrational heat transport in molecular Junctions : Rectification, quantum effects, vibrational mismatch
• Eliminating the cuspidal temperature profile of a non-equilibrium chain
• Novel Fluctuations at a Constrained Liquid-Solid Interface
• Nonequilibrium Green's functions in the study of heat transport of driven nanomechanical systems
• Thermo-mechanical transport in rotor chains
• Heat transport through an open coupled scalar field theory hosting stability-to-instability transition
• Quantum noise theory for phonon transport through nanostructures
• Projective-truncation-approximation study of the one-dimensional ${\varphi }^4$ lattice model
• Super diffusive length dependent thermal conductivity in one-dimensional materials with structural defects: longitudinal to transverse phonon scattering leads to $\kappa \propto L^{1/3}$ law
• Unsteady thermal transport in an instantly heated semi-infinite free end Hooke chain
• Nonlinearity accelerates the thermalization of the quartic FPUT model with stochastic baths
• Localization properties of harmonic chains with correlated mass and spring disorder: Analytical approach
• Cluster sizes in a classical Lennard-Jones chain
• First-principle validation of Fourier's law in d=1,2,3 classical systems
• Optimal qubit-mediated quantum heat transfer via noncommuting operators and strong coupling effects
• Glassy dynamics in strongly anharmonic chains of oscillators
• Diffusive lossless energy and coherence transfer by noisy coupling
• Influence of vortices and phase fluctuations on thermoelectric transport properties of superconductors in a magnetic field
• Thermal rectification in mass-asymmetric one-dimensional anharmonic oscillator lattices with and without a ballistic spacer
• Temperature dependent divergence of thermal conductivity in momentum conserving 1D lattice with asymmetric potential
• Long-range correlations in a simple stochastic model of coupled transport
• Rattling and freezing in a 1-D transport model
• Projection operator approach to master equations for coarse grained occupation numbers in non-ideal quantum gases
• 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 conduction in systems with Kolmogorov-Arnold-Moser phase space structure
• Entropic analysis of the localization-delocalization transition in a one-dimensional correlated lattice
• Theory of Applying Heat Flow from Thermostatted Boundary Walls: Dissipative and Local-Equilibrium Responses and Fluctuation Theorems
• Transport in boundary-driven quantum spin systems: One-way street for the energy current
• Localization of disordered harmonic chain with long-range correlation
• Scaling of energy spreading in a disordered Ding-Dong lattice
• Heat conduction and the nonequilibrium stationary states of stochastic energy exchange processes
• One-dimensional moving window atomistic framework to model long-time shock wave propagation
• Interacting Random Walkers and Non-Equilibrium Fluctuations
• Autonomous Circular Heat Engine
• Heat conduction and diffusion of hard disks in a narrow channel
• Kapitza resistance at a domain boundary in linear and nonlinear chains
• Thermal conductance of suspended nanoribbons: interplay between strain and interatomic potential nonlinearity
• Out-of-equilibrium one-dimensional disordered dipole chain
• Energy flow of moving dissipative topological solitons
• Localization in boundary-driven lattice models
• Contact and Quasi-Static Impact of a Dissipationless Mechanical Model
• Thermally driven classical Heisenberg model in one dimension with a local time-varying field
• Interacting Non-equilibrium Systems with Two Temperatures
• Energy current cumulants in one-dimensional systems in equilibrium
• Low-Temperature Linear Thermal Rectifiers Based on Coriolis forces
• A microscopic model of ballistic-diffusive crossover
• Nanoscale control of heat and spin conductance in artificial spin chains
• Glassy dynamics in disordered oscillator chains
• Slow relaxation in microcanonical warming of a Ising lattice
• Thermodynamics of enhanced heat transfer: a model study
• Violations of local equilibrium and stochastic thermostats
• Thermal rectification in the one-dimensional nonlinearly graded rotor lattice robust in the thermodynamical limit
• Approaching the perfect diode limit through a nonlinear interface
• Heat current magnification in Classical and Quantum spin networks
• Onsager coefficients in a coupled-transport model displaying a condensation transition
• A Symmetry Property of Momentum Distribution Functions in the Nonequilibrium Steady State of Lattice Thermal Conduction
• Local heat current flow in ballistic phonon transport of graphene nanoribbons
• Thermal transport in long-range interacting harmonic chains perturbed by long-range conservative noise
• Anomalous Temperature Induced Transition and Convergence of Thermal Conductivity in Germanene Monolayer
• Energy diffusion in the long-range interacting spin systems
• Lecture notes on large deviations in non-equilibrium diffusive systems
• Nonequilibrium Microscopic Distribution of Thermal Current in Particle Systems
• Aspects of the disordered harmonic chain
• Statistical distribution of bonding distances in a unidimensional solid
• Thermal Transport in Phononic Cayley Tree Networks
• Thermalization with a multibath: an investigation in simple models
• Bifurcation and chaos in one dimensional chains of small particles
• Origin of Temperature Gradient in Nonequilibrium Steady States in Weakly Coupled Quantum Spin Systems
• Collective Transport of Lennard-Jones Particles through One-Dimensional Periodic Potentials
• Thinking transport as a twist
• Random initial data and average shock time in the Fermi-Pasta-Ulam-Tsingou chain
• Neuromorphic heat transport effects in a molecular junction
• Heat conductivity in the presence of a quantized degree of freedom
• Heat rectification by two qubits coupled with Dzyaloshinskii-Moriya interaction
• Resistor-network anomalies in the heat transport of random harmonic chain
• Stochastic Thermodynamics of oscillators networks
• Thermal response of a Fermi-Pasta-Ulam chain with Andersen thermostats
• Thermal transport through a single trapped ion under strong laser illumination
• Energy growth for systems of coupled oscillators with partial damping
• Role of chaos for the validity of statistical mechanics laws: diffusion and conduction
• Nonanomalous heat transport in a one-dimensional composite chain
• Entropic signature of resonant thermal transport: Ordered form of heat conduction
• Nonequilibrium Steady States in the Weakly-Coupled XXZ Model
• Classical and quantum harmonic mean-field models coupled intensively and extensively with external baths
• Weighted average temperature as the effective temperature of a system in contact with two thermal baths
• Thermoelectric properties of Wigner crystal in two-dimensional periodic potential
• Thermal transport in disordered harmonic chains revisited: Formulation of thermal conductivity and local temperatures
• Heat transport in a three dimensional slab geometry and the temperature profile of Ingen-Hausz's experiment
• Molecular hints of two-step transition to convective flow via streamline percolation
• Thermal conductivity and local thermodynamic equilibrium of stochastic energy exchange models
• Unifying renormalized and bare viscosity in two-dimensional molecular dynamics simulations
• From Near-Integrable to Far-from-Integrable: A Unified Picture of Thermalization and Heat Transport
• Quantum vs Classical Thermal Transport at Low Temperatures
• Nonlinearity-induced transition in heat conduction through a topological metamaterial of rotors
• Dephasing-assisted macrospin transport
• Collisional relaxation and dynamical scaling in multiparticle collisions dynamics
• Construction of cubic nonlinear lattice free from umklapp processes
• Computing Nonequilibrium Transport from Short-Time Transients: From Lorentz Gas to Heat Conduction in One Dimensional Chains
• Strong overlap of deterministic and stochastic dynamics in a super-diffusive regime
• Dephasing enhanced transport in boundary-driven quasiperiodic chains
• Infinite-temperature thermostats by energy localization in a nonequilibrium setup