Thermal conduction in classical low-dimensional lattices

  title={Thermal conduction in classical low-dimensional lattices},
  author={Stefano Lepri and Roberto Livi and Antonio Politi},
  journal={Physics Reports},
Dynamics, kinetics, and transport properties of the one-dimensional mass-disordered harmonic lattice.
The dynamics, kinetics, and the transport properties of the one-dimensional (1D) mass-disordered lattice of harmonic oscillators with the number of particles N < or =5000 and two accurate methods to calculate the temporal behavior of pair correlation functions were developed.
Heat transport in low-dimensional systems
Recent results on theoretical studies of heat conduction in low-dimensional systems are presented. These studies are on simple, yet non-trivial, models. Most of these are classical systems, but some
Unsteady ballistic heat transport: linking lattice dynamics and kinetic theory
The kinetic theory is widely used in the description of thermal transport at the micro- and nanoscale. In the theory, it is assumed that heat is carried by quasi-particles, obeying the Boltzmann
Heat flux in one-dimensional systems.
This work revisits the problem of heat conduction in chains of classical nonlinear oscillators, following a Lagrangian and a Eulerian approach, and finds that the convective component tends to be negative in the presence of a negative pressure.
Fluctuations in and out of equilibrium: Thermalization, quantum measurements and Coulomb disorder
This purely theoretical thesis covers aspects of two contemporary research fields: the non-equilibrium dynamics in quantum systems and the electronic properties of three-dimensional topological
Beyond phonon hydrodynamics: Nonlocal phonon heat transport from spatial fractional-order Boltzmann transport equation
Spatially convoluting formulations have been used to describe nonlocal thermal transport, yet there is no related investigation at the microscopic level such as the Boltzmann transport theory. The
Nonequilibrium dynamics of a stochastic model of anomalous heat transport
We study the dynamics of covariances in a chain of harmonic oscillators with conservative noise in contact with two stochastic Langevin heat baths. The noise amounts to random collisions between
Dimensional crossover of thermal transport in quantum harmonic lattices coupled to self-consistent reservoirs.
Criteria derived for quantum-mechanical lattices imply that normal transport emerges in high enough dimensions despite total momentum conservation and reinforce the prevailing conjecture deduced in the classical limit.
Fast and slow thermal processes in harmonic scalar lattices.
  • V. Kuzkin, A. Krivtsov
  • Physics
    Journal of physics. Condensed matter : an Institute of Physics journal
  • 2017
Numerical simulations show that presented theory describes the evolution of temperature field at short and large time scales with high accuracy, and demonstrates that these processes are irreversible.


Heat Conduction in Two-Dimensional Nonlinear Lattices
The divergence of the heat conductivity in the thermodynamic limit is investigated in 2d-lattice models of anharmonic solids with nearest-neighbour interaction from single-well potentials. Two
Memory effects and heat transport in one-dimensional insulators
Abstract:We study the dynamical correlation functions and heat conduction for the simplest model of quasi one-dimensional (1d) dielectric crystal i.e. a chain of classical particles coupled by
Chaotic behavior in nonlinear Hamiltonian systems and equilibrium statistical mechanics
The relation between chaotic dynamics of nonlinear Hamiltonian systems and equilibrium statistical mechanics in its canonical ensemble formulation has been investigated for two different nonlinear
Non-Equilibrium Statistical Mechanics of Anharmonic Chains Coupled to Two Heat Baths at Different Temperatures
Abstract:We study the statistical mechanics of a finite-dimensional non-linear Hamiltonian system (a chain of anharmonic oscillators) coupled to two heat baths (described by wave equations). Assuming
Energy transport and detailed verification of Fourier heat law in a chain of colliding harmonic oscillators
The authors study a simple nonlinear classical Hamiltonian system with positive K-entropy, a model for heat conduction, and they find that it obeys the Fourier heat law. Numerical simulation of its
Heat Conduction in Chains of Nonlinear Oscillators
The approach to nonequilibrium statistical mechanicsthrough the introduction of microscopically time-reversible models has been shown to be rather powerfulin the context of many-particle dynamics
Abnormal Lattice Thermal Conductivity of a One‐Dimensional, Harmonic, Isotopically Disordered Crystal
Energy transport is investigated in a model system for which exact analytic results can be obtained. The system is an infinite, one‐dimensional harmonic crystal which is perfect everywhere except in
Finite thermal conductivity in 1D lattices
We discuss the thermal conductivity of a chain of coupled rotators, showing that it is the first example of a 1D nonlinear lattice exhibiting normal transport properties in the absence of an on-site
Thermal conductivity in a chain of alternately free and bound particles
The thermal conductivity k of a lattice of alternately free and harmonically bound particles placed between two temperature reservoirs is calculated for various chain lengths and dimensionless energy