From Normal Diffusion to Superdiffusion of Energy in the Evanescent Flip Noise Limit

We consider a harmonic chain perturbed by a stochastic noise which conserves the energy and a second quantity called the volume, and destroys all the other ones. We then add to this model a second energy conserving noise depending on a parameter $$\gamma $$γ, that annihilates the volume conservation. When $$\gamma $$γ is of order one, the energy diffuses according to the standard heat equation after a space-time diffusive scaling. On the other hand, when $$\gamma =0$$γ=0, the energy superdiffuses according to a $$3/4$$3/4-fractional heat equation after a subdiffusive space-time scaling. In this paper, we study the existence of a crossover between these two regimes as a function of $$\gamma $$γ.