OLLA , Stefano

We consider a one-dimensional unpinned chain of harmonic oscillators with random masses.We prove that after hyperbolic scaling of space and time the distributions of the elongation, momentum and energy converge to the solution of the Euler equations. Anderson localization decouples the mechanical modes from the thermal modes, allowing the...

We consider the macroscopic limit for the space-time density fluctuations in the open symmetric simple exclusion in the quasi-static scaling limit. We prove that the distribution of these fluctuations converge to a gaussian space-time field that is delta correlated in time but with long-range correlations in space.

We consider the macroscopic limit for the space-time density fluctuations in the open symmetric simple exclusion in the quasi-static scaling limit. We prove that the distribution of these fluctuations converge to a gaussian space-time field that is delta correlated in time but with long-range correlations in space.

We consider an infinite system of cells coupled into a chain by a smooth nearest neighbor potential $\ve V$. The uncoupled system (cells) evolve according to Hamiltonian dynamics perturbed stochastically with an energy conserving noise of strenght $\noise$. We study the Green-Kubo (GK) formula $\kappa(\ve,\noise)$ for the heat conductivity of...

We study the Green-Kubo (GK) formula κ(ε,ξ) for the heat conductivity of an infinite chain of d-dimensional finite systems (cells) coupled by a smooth nearest neighbour potential εV. The uncoupled systems evolve according to Hamiltonian dynamics perturbed stochastically by an energy conserving noise of strength ξ. Noting that κ(ε,ξ) exists and...

We consider an infinite system of cells coupled into a chain by a smooth nearest neighbor potential $\ve V$. The uncoupled system (cells) evolve according to Hamiltonian dynamics perturbed stochastically with an energy conserving noise of strenght $\noise$. We study the Green-Kubo (GK) formula $\kappa(\ve,\noise)$ for the heat conductivity of...

We review recent rigorous mathematical results about the macroscopic behaviour of harmonic chains with the dynamics perturbed by a random exchange of velocities between nearest neighbor particles. The random exchange models the effects of nonlinearities of anharmonic chains and the resulting dynamics have similar macroscopic behaviour. In...