Stefano Olla

Large deviations for Gibbs random fields

A large deviation principle for Gibbs random fields on Zd is proven and a corresponding large deviations proof of the Gibbs variational formula is given. A generalization of the Lanford theory of large deviations is also obtained.

Momentum conserving model with anomalous thermal conductivity in low dimensional systems

Anomalous large thermal conductivity has been observed numerically and experimentally in one- and two-dimensional systems. There is an open debate about the role of conservation of momentum. We introduce a model whose thermal conductivity diverges in dimensions 1 and 2 if momentum is conserved, while it remains finite in dimension d > or = 3. We consider a system of harmonic oscillators perturbed by a nonlinear stochastic dynamics conserving momentum and energy. We compute explicitly the time correlation function of the energy current C(J)(t), and we find that it behaves, for large time, like t(-d/2) in the unpinned cases, and like t(-d/2-1) when an on-site harmonic potential is present. This result clarifies the role of conservation of momentum in the anomalous thermal conductivity in low dimensions.

Thermal Conductivity for a Momentum Conservative Model

We introduce a model whose thermal conductivity diverges in dimension 1 and 2, while it remains finite in dimension 3. We consider a system of oscillators perturbed by a stochastic dynamics conserving momentum and energy. We compute thermal conductivity via Green-Kubo formula. In the harmonic case we compute the current-current time correlation function, that decay like t−d/2 in the unpinned case and like t−d/2–1 if an on-site harmonic potential is present. This implies a finite conductivity in d ≥ 3 or in pinned cases, and we compute it explicitly. For general anharmonic strictly convex interactions we prove some upper bounds for the conductivity that behave qualitatively as in the harmonic cases.

Fluctuations for ∇φ interface model on a wall

We consider [backward difference][phi] interface model on a hard wall. The hydrodynamic large-scale space-time limit for this model is discussed with periodic boundary by Funaki et al. (2000, preprint). This paper studies fluctuations of the height variables around the hydrodynamic limit in equilibrium in one dimension imposing Dirichlet boundary conditions. The fluctuation is non-Gaussian when the macroscopic interface is attached to the wall, while it is asymptotically Gaussian when the macroscopic interface stays away from the wall. Our basic method is the penalization. Namely, we substitute in the dynamics the reflection at the wall by strong drift for the interface when it goes down beyond the wall and show the fluctuation result for such massive [backward difference][phi] interface model. Then, this is applied to prove the fluctuation for the [backward difference][phi] interface model on the wall.

Energy Transport in Stochastically Perturbed Lattice Dynamics

We consider lattice dynamics with a small stochastic perturbation of order

On homogenization of time-dependent random flows

{\varepsilon}

Superdiffusion of Energy in a Chain of Harmonic Oscillators with Noise

and prove that for a space–time scale of order