# Soutenances de Thèses 2017

**Xiangyu CAO**

*24 mars 2017*

*Salle des Conseils de l'IPN*

**Soutenance de thèse**

**Soutenance de thèse**

**Disordered statistical physics in low dimensions: extremes, glass transition, and localization.**

**Disordered statistical physics in low dimensions: extremes, glass transition, and localization.**

This thesis presents original results in two domains of disordered statistical physics: logarithmic correlated Random Energy Models (logREMs), and localization transitions in long-range random matrices.

In the first part devoted to logREMs, we show how to characterize their common properties and model--specific data. Then we develop their replica symmetry breaking treatment, which leads to the freezing scenario of their free energy distribution and the general description of their minima process, in terms of decorated Poisson point process. We also report a series of new applications of the Jack polynomials in the exact predictions of some observables in the circular model and its variants. Finally, we present the recent progress on the exact connection between logREMs and the Liouville conformal field theory.

The goal of the second part is to introduce and study a new class of banded random matrices, the broadly distributed class, which is characterid an effective sparseness. We will first study a specific model of the class, the Beta Banded random matrices, inspired by an exact mapping to a recently studied statistical model of long--range first--passage percolation/epidemics dynamics. Using analytical arguments based on the mapping and numerics, we show the existence of localization transitions with mobility edges in the ``stretch--exponential'' parameter--regime of the statistical models. Then, using a block--diagonalization renormalization approach, we argue that such localization transitions occur generically in the broadly distributed class.

The defense presentation will focus on the logREM--Liouville connection and the broadly distributed random matrices.

Directeurs de thèse: Alberto Rosso, Raoul Santachiara

Jury: Bertrand Georgeot, Jonathan Keating, Christopher Mudry, Didina Serban; invité: Pierre Le Doussal

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**Aleksey FEDOROV**

*28 juin 2017*

*Auditorium Irène Joliot-Curie de l'IPN*

**Soutenance de thèse**

**Soutenance de thèse**

**Non-conventional many-body phases in ultracold dipolar systems**

**Non-conventional many-body phases in ultracold dipolar systems**

The problem of revealing and describing novel macroscopic quantum states characterized by exotic and non-conventional properties has the fundamental importance for modern physics. Such states offer fascinating prospects for potential applications in quantum information processing, quantum simulation, and material research. In the present Thesis we develop a theory for describing non-conventional phases of ultracold dipolar gases. The related systems of large-spin atoms, polar molecules, and dipolar excitons in semiconductors are actively studied in experiments. We put the main emphasis on revealing the role of the long-range character of the dipole-dipole interaction. We consider the effect of rotonization for a 2D weakly interacting gas of tilted dipolar bosons in a homogeneous layer, and demonstrate that in contrast to the case of perpendicular dipoles, in a wide range of tilting angles the condensate depletion remains small even when the roton minimum is extremely close to zero. We predict the effect of rotonization for a weakly correlated Bose gas of dipolar excitons in a semiconductor layer and calculate the stability diagram. According to our estimates, the threshold of the roton instability for a bose-condensed exciton gas with the roton-maxon spectrum is achievable experimentally in semiconductor layers. We then consider p-wave superfluids of identical fermions in 2D lattices. The optical lattice potential manifests itself in an interplay between an increase in the density of states on the Fermi surface and the modification of the fermion-fermion interaction (scat- tering) amplitude. The density of states is enhanced due to an increase of the effective mass of atoms. For short-range interacting atoms in deep lattices the scattering amplitude is strongly reduced compared to free space due to a small overlap of wavefunctions of fermions sitting in the neighboring lattice sites, which suppresses the p-wave superfluidity. However, we show that for a moderate lattice depth there is still a possibility to create p-wave superfluids with sizable transition temperatures. For fermionic polar molecules, due to a long-range character of the dipole-dipole interaction the effect of the suppression of the scattering amplitude is absent. It is shown that for microwave-dressed polar molecules a stable topological p+ip superfluid may emerge in the 2D lattice at realistic temperatures. Finally, we discuss another interesting novel superfluid of fermionic polar molecules. It is expected in a bilayer system, where dipoles are oriented perpendicularly to the layers and in opposite directions in different layers. We demonstrate the emergence of interlayer superfluid pairing. In contrast to the already known s-wave interlayer superfluid, when all dipoles are parallel to each other, in our case the s-wave pairing is suppressed and there can be p-wave or higher partial wave superfluids.

Directeurs de thèse: Georgy Shlyapnikov

Jury: Christophe Texier, Mikhail Baranov, Paolo Pedri, Andrey Varlamov