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

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

2008-09-02

arxiv.org/abs/0809.0453v2

J. Phys. A: Math. Theor. 42 (2009) 025001

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1088/1751-8113/42/2/025001

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 $N$.

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