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

• Published in: Journal of physics. A, Mathematical and theoretical Vol. 42; no. 2; pp. 025001 - 025001 (15)
• Main Authors: Lepri, S, Mejía-Monasterio, C, Politi, A
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 16.01.2009; IOP
• Subjects: Exact sciences and technology; Physics; Stochastic model; Numerical solution; Anomalous transport; Thermodynamic limit; Covariance matrices; Analytical solution; Oscillators
• ISSN: 1751-8121; 1751-8113; 1751-8121
• DOI: 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 - > {infinity}). 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. Our theoretical results are finally found to be consistent with the numerical solutions of the covariance matrix for finite N.