RABAHI Yaniss : Glass transition between a superfluid and a Bose glass in ultracold atomic gases

Résumé de thèse :

Understanding the interplay between interactions and disorder is one of the major challenges in condensed matter physics. For interacting bosons, describing superfluid helium and cold atoms experiments, disorder induces a quantum phase transition from a superfluid to a localized phase, the Bose glass. The properties of this phase, and the transition itself, have yet to be qualitatively understood theoretically, although recent progress have been made using numerical simulations. There are still many open questions about this transition, such as a theoretical characterization of the critical exponents, especially the dynamical exponent (which has been conjectured to be equal to the number of dimensions of the system), or the existence of an upper critical dimension. A promising avenue is to use the Functional Renormalization Group (FRG), a modern version of Wilson's Renormalization Group, which allows for non-perturbative approximation schemes. The goal of the PhD thesis is to study the superfluid Bose-glass transition in the framework of the FRG. This will involve deriving the FRG flow equation in an appropriate approximation scheme and solving the corresponding integrodifferential equations. Beyond characterizing the transition, this should also shed light on the properties of the Bose glass phase.

Doctorant : RABAHI Yaniss

Directeur de thèse : RANÇON Adam