A Stochastic Model of Anomalous Heat Transport

Mar 17, 2010, 12:15 PM
Nordita Seminar Room 132:028 (Nordita)

Nordita Seminar Room 132:028



Carlos Mejia-Monasterio


Abstract: We investigate the non-equilibrium dynamics of a chain of harmonic oscillators in contact with two stochastic Langevin heat baths at different temperatures and undergoing random collisions between neighbours that exchange their momenta with a constant rate $\gamma$. By means of an appropriate continuum limit, we solve the equations for the covariance matrix to leading order in the stationary state, and derive exact expressions for the temperature profile and for the leading contribution of the energy current, which scales as $1/\sqrt{\gamma N}$. At finite times, we solve adiabatically the equation describing the time evolution of the temperature profile $T(y,t)$, obtaining that in the bulk of the system, $T(y)$ evolves according to the energy continuity equation, but with a space-time scaling that is described by a fractional diffusion equation.

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