On the derivation of Fourier's law for coupled anharmonic oscillators
arXiv:math-ph/0605062
Abstract
We study the Hamiltonian system made of weakly coupled anharmonic oscillators arranged on a three dimensional lattice and subjected to a stochastic forcing mimicking heat baths of temperatures T_1 and T_2 on the hyperplanes at x_1=0 and N. We introduce a truncation of the Hopf equations describing the stationary state of the system which leads to a nonlinear equation for the two-point stationary correlation functions. We prove that these equations have a unique solution which, for N large, is approximately a local equlibrium state satisfying Fourier law that relates the heat current to a local temperature gradient. The temperature exhibits a nonlinear profile.
arXiv comment69 pages
References in corpus (15)
- Anomalous heat conduction in one dimensional momentum-conserving systems
- Non-Equilibrium Statistical Mechanics of Anharmonic Chains Coupled to Two Heat Baths at Different Temperatures
- On the anomalous thermal conductivity of one-dimensional lattices
- A momentum conserving model with anomalous thermal conductivity in low dimension
- Non-Equilibrium Statistical Mechanics of Strongly Anharmonic Chains of Oscillators
- Entropy Production in Non-Linear, Thermally Driven Hamiltonian Systems
- Fermi-Pasta-Ulam lattice: Peierls equation and anomalous heat conductivity
- Exponential Convergence to Non-Equilibrium Stationary States in Classical Statistical Mechanics
- Thermal Conductivity for a Momentum Conserving Model
- Energy Transport in Weakly Anharmonic Chains
- Asymptotic Behavior of Thermal Non-Equilibrium Steady States for a Driven Chain of Anharmonic Oscillators
- Nonequilibrium Energy Profiles for a Class of 1-D Models
- Non-Equilibrium Statistical Mechanics of Classical Lattice Field Theory
- Normal Heat Conductivity in a strongly pinned chain of anharmonic oscillators
- Temperature Profiles in Hamiltonian Heat Conduction