Energy Transport in Weakly Anharmonic Chains

Abstract

We investigate the energy transport in a one-dimensional lattice of oscillators with a harmonic nearest neighbor coupling and a harmonic plus quartic on-site potential. As numerically observed for particular coupling parameters before, and confirmed by our study, such chains satisfy Fourier's law: a chain of length N coupled to thermal reservoirs at both ends has an average steady state energy current proportional to 1/N. On the theoretical level we employ the Peierls transport equation for phonons and note that beyond a mere exchange of labels it admits nondegenerate phonon collisions. These collisions are responsible for a finite heat conductivity. The predictions of kinetic theory are compared with molecular dynamics simulations. In the range of weak anharmonicity, respectively low temperatures, reasonable agreement is observed.

25 pages, 10 figures

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Cited by in corpus (42)

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• Lieb-Robinson Bounds for Harmonic and Anharmonic Lattice Systems
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• Nonequilibrium Green's function method for thermal transport in junctions
• Effect of phonon-phonon interactions on localization
• Energy carriers in the Fermi-Pasta-Ulam $\beta$ lattice: Solitons or Phonons?
• Sufficient conditions for thermal rectification in graded materials
• Double scaling in the relaxation time in the $\beta$-FPUT model
• Anomalous energy transport in the FPU-beta chain
• Thermal Rectification in Graded Materials
• Energy transfer in a fast-slow Hamiltonian system
• Fourier's Law from Closure Equations
• Large deviations of lattice Hamiltonian dynamics coupled to stochastic thermostats
• Transition from diffusive to ballistic dynamics for a class of finite quantum models
• Wave Turbulence and thermalization in one-dimensional chains
• Non-equilibrium steady states for chains of four rotors
• Coexistence of ballistic and Fourier regimes in the $\beta$-FPUT lattice
• Energy separation in oscillatory Hamiltonian systems without any non-resonance condition
• Fourier's law based on microscopic dynamics
• Wick polynomials and time-evolution of cumulants
• Drastic fall-off of the thermal conductivity for disordered lattices in the limit of weak anharmonic interactions
• Thermal rectification in anharmonic chains under an energy-conserving noise
• Heat wave propagation in a nonlinear chain
• Thermal Conductivity for a Noisy Disordered Harmonic Chain
• Heat conductivity from molecular chaos hypothesis in locally confined billiard systems
• Kinetic theory of phonons in weakly anharmonic particle chains
• Convergence of a kinetic equation to a fractional diffusion equation
• Dynamics and transport in the boundary-driven dissipative Klein-Gordon chain
• Hot scatterers and tracers for the transfer of heat in collisional dynamics
• Quantitative Rates of Convergence to Non-Equilibrium Steady State for a Weakly Anharmonic Chain of Oscillators
• Boltzmann equation approach to transport in finite modular quantum systems
• Thermalization of oscillator chains with onsite anharmonicity and comparison with kinetic theory
• On the derivation of Fourier's law for coupled anharmonic oscillators
• On the Boltzmann Equation for Weakly Nonlinear Wave Equations
• On the local space-time structure of non-equilibrium steady states
• Glassy dynamics in strongly anharmonic chains of oscillators
• Projective-truncation-approximation study of the one-dimensional ${\varphi }^4$ lattice model
• Projection operator approach to master equations for coarse grained occupation numbers in non-ideal quantum gases
• Approaching the perfect diode limit through a nonlinear interface
• Small perturbation of a disordered harmonic chain by a noise and an anharmonic potential
• Dephasing enhanced transport in boundary-driven quasiperiodic chains