A stochastic model of anomalous heat transport: analytical solution of the steady state

Abstract

We consider a one-dimensional harmonic crystal with conservative noise, in contact with two stochastic Langevin heat baths at different temperatures. The noise term consists of collisions between neighbouring oscillators that exchange their momenta, with a rate $\gamma$. The stationary equations for the covariance matrix are exactly solved in the thermodynamic limit ($N\to \infty$). In particular, we derive an analytical expression for the temperature profile, which turns out to be independent of $\gamma$. Moreover, we obtain an exact expression for the leading term of the energy current, which scales as $1/\sqrt{\gamma N}$. Our theoretical results are finally found to be consistent with the numerical solutions of the covariance matrix for finite $N$.

Minor changes in the text. To appear in Journal of Physics A

References in corpus (8)

• A momentum conserving model with anomalous thermal conductivity in low dimension
• Heat transport in harmonic lattices
• Stochastic interacting particle systems out of equilibrium
• Fourier's Law for a Harmonic Crystal with Self-consistent Stochastic Reservoirs
• Duality and exact correlations for a model of heat conduction
• Heat conduction and Fourier's law by consecutive local mixing and thermalization
• Fourier's Law from Closure Equations
• Nonequilibrium Invariant Measure under Heat Flow

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