3/4 Fractional superdiffusion of energy in a system of harmonic oscillators perturbed by a conservative noise

Cedric Bernardin (1) , Patricia Gonçalves (2, 3) , Milton Jara (4)

1 LJAD - Laboratoire Jean Alexandre Dieudonné
2 CMAT - Centro de Matemática [Minho]
3 PUC-Rio - Departamento de Informática = Department of Informatics
4 IMPA - Instituto Nacional de Matemática Pura e Aplicada

We consider a harmonic chain perturbed by an energy conserving noise and show that after a space-time rescaling the energy-energy correlation function is given by the solution of a skew-fractional heat equation with exponent 3/4.

Domaines: Mécanique statistique [cond-mat.stat-mech]; Probabilités [math.PR]

Cedric Bernardin, Patricia Gonçalves, Milton Jara. 3/4 Fractional superdiffusion of energy in a system of harmonic oscillators perturbed by a conservative noise. Archive for Rational Mechanics and Analysis, 2016, 220 (2), pp.505--542. ⟨10.1007/s00205-015-0936-0⟩. ⟨hal-00943116v3⟩