Macroscopic evolution of mechanical and thermal energy in a harmonic chain with random flip of velocities

Tomasz Komorowski; Stefano Olla; Marielle Simon

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arXiv · 1609.02413

Macroscopic evolution of mechanical and thermal energy in a harmonic chain with random flip of velocities

Tomasz Komorowski·Stefano Olla·Marielle Simon

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Abstract

We consider an unpinned chain of harmonic oscillators with periodic boundary conditions, whose dynamics is perturbed by a random flip of the sign of the velocities. The dynamics conserves the total volume (or elongation) and the total energy of the system. We prove that in a diffusive space-time scaling limit the profiles corresponding to the two conserved quantities converge to the solution of a diffusive system of differential equations. While the elongation follows a simple autonomous linear diffusive equation, the evolution of the energy depends on the gradient of the square of the elongation.

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Tomasz Komorowski, Stefano Olla, Marielle Simon. 2016-09-08. Macroscopic evolution of mechanical and thermal energy in a harmonic chain with random flip of velocities. https://arxiv.org/abs/1609.02413

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