title: Fourier's law from a chain of coupled planar harmonic oscillators under energy-conserving noise.
abstract: We study the transport of heat along a chain of particles interacting through a harmonic potential and subject to heat reservoirs at its ends. Each particle has two degrees of freedom and is subject to a stochastic noise that produces infinitesimal changes in the velocity while keeping the kinetic energy unchanged. This is modeled by means of a Langevin equation with multiplicative noise. We show that the introduction of this energy-conserving stochastic noise leads to Fourier's law. By means of an approximate solution that becomes exact in the thermodynamic limit, we also show that the heat conductivity κ behaves as κ = aL/(b + λL) for large values of the intensity λ of the energy-conserving noise and large chain sizes L. Hence, we conclude that in the thermodynamic limit the heat conductivity is finite and given by κ = a/λ.
authors.affiliation: Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, Santo André, São Paulo 09210-170, Brazil and Instituto de Física, Universidade de São Paulo, Caixa Postal 66318, 05314-970 São Paulo, Brazil.
authors.forename: Gabriel T
authors.initials: GT
authors.lastname: Landi
authors.affiliation: Instituto de Física, Universidade de São Paulo, Caixa Postal 66318, 05314-970 São Paulo, Brazil.
authors.forename: Mário J
authors.initials: MJ
authors.lastname: de Oliveira
mesh_terms: D003198:Computer Simulation; D004735:Energy Transfer; D005246:Feedback; D005583:Fourier Analysis; D008956:Models, Chemical; D015233:Models, Statistical; D013269:Stochastic Processes; D013814:Thermal Conductivity; D013816:Thermodynamics