Dafne Prado & Pierre-Louis Taillat

- Dafne Prado : Anderson localization on Husimi trees and its implications for many-body localization

Motivated by the analogy between many-body localization and Anderson localization on the Bethe lattice and related hierarchical graphs, we investigate the role of local loops and correlations, two structural features of many-body configuration spaces that are absent from the Bethe lattice. We first study localization on the Husimi tree, a generalization of the Bethe lattice containing a finite density of local loops of arbitrary but finite length. The exact cavity treatment of the model provides a controlled framework to systematically assess the effect of loop topology on localization. We find that local loops enhance resonant processes, thereby reducing the critical disorder as their number and size increase. At the same time, they promote local hybridization, leading to an increase in the spatial extent of localized eigenstates. We then generalize the model by introducing random hopping amplitudes with local correlations between neighboring hoppings. Preliminary results indicate that these correlations also reduce the critical disorder. These results suggest that both loops and local correlations are essential ingredients for bringing single-particle localization models on hierarchical graphs closer to the structure and phenomenology of many-body configuration spaces.

- Pierre-Louis Taillat : Hydrodynamical transport in a low temperature Fermi gas

The study of Fermi liquids has seen a resurgence with the cold atom experiments. These systems are clean and easy to control, making it possible to study them from both a thermodynamic and a dynamic perspective. More specifically, it is possible to measure transport coefficients such as viscosity, spin diffusivity, or specific heat. A theory often used to describe Fermi liquids is Landau's theory of Fermi liquids. It is based on the concept of quasiparticles and on a semi-classical action. However, it has structural limitations that we will attempt to overcome in this presentation by introducing a quantized Landau theory that unifies all low-energy phenomena in weakly interacting fermionic systems. We will apply this theory to transport, and we will show that, in the hydrodynamic limit, the Navier-Stokes equations arise naturally.