Heat flow in a periodically forced, unpinned thermostatted chain
Résumé
We prove the hydrodynamic limit for a one-dimensional harmonic chain of interacting atoms with a random flip of the momentum sign. The system
is open: at the left boundary it is attached to a heat bath at temperature T_,
while at the right endpoint it is subject to an action of a force which reads as
$F + n^{-1/2}F̃(n^2 t)$, where F ⩾ 0 and F̃(t) is a periodic function. Here n is the size of the microscopic system. Under a diffusive scaling of space-time, we prove that the empirical profiles of the two locally conserved quantities – the volume stretch and the energy – converge, as n → +∞, to the solution of a non-linear diffusive system of conservative partial differential equations with a Dirichlet type and Neumann boundary conditions on the left and the right endpoints, respectively.
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