71 citations · 752 across the 67 of their papers we have counts for
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Free-energy variations for determinantal 2D plasmas with holes
Nicolas Rougerie
We study the Gibbs equilibrium of a classical 2D Coulomb gas in the determinantal case = 2. The external potential is the sum of a quadratic term and the potential generated by…
Quantum Hall Phases of Cold Bose Gases
Nicolas Rougerie, Jakob Yngvason
Cold atomic gases of interacting bosons subject to rapid rotation and confined in anharmonic traps can theoretically exhibit analogues of the fractional quantum Hall effect for ele…
A Lieb-Thirring inequality for extended anyons
Théotime Girardot, Nicolas Rougerie
We derive a Pauli exclusion principle for extended fermion-based anyons of any positive radius and any non-trivial statistics parameter. That is, we consider 2D fermionic particles…
Thomas-Fermi profile of a fast rotating Bose-Einstein condensate
Dinh-Thi Nguyen, Nicolas Rougerie
We study the minimizers of a magnetic 2D non-linear Schrödinger energy functional in a quadratic trapping potential, describing a rotating Bose-Einstein condensate. We derive an ef…
Quantum statistics transmutation via magnetic flux attachment
Gaultier Lambert, Douglas Lundholm, Nicolas Rougerie
We consider a model for two types (bath and tracers) of 2D quantum particles in a perpendicular magnetic field. Interactions are short range and inter-species, and we assume that t…
Bosons in a double well: two-mode approximation and fluctuations
Alessandro Olgiati, Nicolas Rougerie, Dominique Spehner
We study the ground state for many interacting bosons in a double-well potential, in a joint limit where the particle number and the distance between the potential wells both go to…
Semiclassical limit for almost fermionic anyons
Théotime Girardot, Nicolas Rougerie
In two-dimensional space there are possibilities for quantum statistics continuously interpolating between the bosonic and the fermionic one. Quasi-particles obeying such statistic…
On the Laughlin function and its perturbations
Nicolas Rougerie
The Laughlin state is an ansatz for the ground state of a system of 2D quantum particles submitted to a strong magnetic field and strong interactions. The two effects conspire to g…
Stability of the Laughlin phase against long-range interactions
Alessandro Olgiati, Nicolas Rougerie
A natural, "perturbative", problem in the modelization of the fractional quantum Hall effect is to minimize a classical energy functional within a variational set based on Laughlin…
Derivation of renormalized Gibbs measures from equilibrium many-body quantum Bose gases
Mathieu Lewin, Phan Thành Nam, Nicolas Rougerie
We review our recent result on the rigorous derivation of the renormalized Gibbs measure from the many-body Gibbs state in 1D and 2D. The many-body renormalization is accomplished…
Limites de champ moyen bosoniques {à} temp{é}rature positive
Nicolas Rougerie
I present recent results in quantum statistical mechanics, obtained in joint works with Mathieu Lewin and Phan Th{à}nh Nam. We consider a certain mean-field limit of the grand-cano…
On the stability of 2D dipolar Bose-Einstein condensates
Arnaud Eychenne, Nicolas Rougerie
We study the existence of energy minimizers for a Bose-Einstein condensate with dipole-dipole interactions, tightly confined to a plane. The problem is critical in that the kinetic…
The interacting 2D Bose gas and nonlinear Gibbs measures
Mathieu Lewin, Phan Thành Nam, Nicolas Rougerie
We announce a new theorem bearing on high-temperature 2D Bose gases. In a certain mean-field-like regime, the grand-canonical quantum Gibbs state reduces to a nonlinear Gibbs measu…
The Laughlin liquid in an external potential
Nicolas Rougerie, Jakob Yngvason
We study natural perturbations of the Laughlin state arising from the effects of trapping and disorder. These are N-particle wave functions that have the form of a product of Laugh…
Gibbs measures based on 1D (an)harmonic oscillators as mean-field limits
Mathieu Lewin, Phan Thành Nam, Nicolas Rougerie
We prove that Gibbs measures based on 1D defocusing nonlinear Schr{ö}dinger functionals with sub-harmonic trapping can be obtained as the mean-field/large temperature limit of the…
Local incompressibility estimates for the Laughlin phase
Elliott Lieb, Nicolas Rougerie, Jakob Yngvason
We prove sharp density upper bounds on optimal length-scales for the ground states of classical 2D Coulomb systems and generalizations thereof. Our method is new, based on an auxil…
Interacting bosons in a double-well potential : localization regime
Nicolas Rougerie, Dominique Spehner
We study the ground state of a large bosonic system trapped in a symmetric double-well potential, letting the distance between the two wells increase to infinity with the number of…
Local density approximation for the almost-bosonic anyon gas
Michele Correggi, Douglas Lundholm, Nicolas Rougerie
We study the minimizers of an energy functional with a self-consistent magnetic field, which describes a quantum gas of almost-bosonic anyons in the average-field approximation. Fo…
Rigidity of the Laughlin liquid
Elliott Lieb, Nicolas Rougerie, Jakob Yngvason
We consider general N-particle wave functions that have the form of a product of the Laughlin state with filling factor and an analytic function of the N variables. This i…
Some contributions to many-body quantum mathematics
Nicolas Rougerie
The results summarized here are intended as rigorous mathematical statements on various physical models coming from condensed matter physics, statistical mechanics (classical and q…
Bose Gases at Positive Temperature and Non-Linear Gibbs Measures
Mathieu Lewin, Phan Thành Nam, Nicolas Rougerie
We summarize recent results on positive temperature equilibrium states of large bosonic systems. The emphasis will be on the connection between bosonic grand-canonical thermal stat…
Effects of boundary curvature on surface superconductivity
Michele Correggi, Nicolas Rougerie
We investigate, within 2D Ginzburg-Landau theory, the ground state of a type-II superconducting cylinder in a parallel magnetic field varying between the second and third critical…
A note on 2D focusing many-boson systems
Mathieu Lewin, Phan Thành Nam, Nicolas Rougerie
We consider a 2D quantum system of bosons in a trapping potential , interacting via a pair potential of the form . We show that for all $0 \textless{}…
From Bosonic Grand-Canonical Ensembles to Nonlinear Gibbs Measures
Nicolas Rougerie
In a recent paper, in collaboration with Mathieu Lewin and Phan Th{à}nh Nam, we showed that nonlinear Gibbs measures based on Gross-Pitaevskii like functionals could be derived fro…