Macroscopic evolution of mechanical and thermal energy in a harmonic   chain with random flip of velocities
  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. 
Tomasz Komorowski, Stefano Olla, Marielle Simon
math.PR cond-mat.stat-mech math-ph math.MP