A stochastic model of anomalous heat transport: analytical solution of the steady state - Condensed Matter > Statistical Mechanics

Abstract: We consider a one-dimensional harmonic crystal with conservative noise, incontact with two stochastic Langevin heat baths at different temperatures.
Thenoise term consists of collisions between neighbouring oscillators thatexchange their momenta, with a rate $\gamma$.
The stationary equations for thecovariance 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 exactexpression for the leading term of the energy current, which scales as$1-\sqrt{\gamma N}$.
Our theoretical results are finally found to be consistentwith the numerical solutions of the covariance matrix for finite $N$.

Author: Stefano Lepri, Carlos Mejia-Monasterio, Antonio Politi

Source: https://arxiv.org/