71 citations · 752 across the 67 of their papers we have counts for
76 papers
theory limit of a many-body bosonic free energy
Lucas Jougla, Nicolas Rougerie
We consider the quantum Gibbs state of an interacting Bose gas on the 2D torus. We set temperature, chemical potential and coupling constant in a regime where classical field theor…
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…
The 2D Chern-Simons-Schr{ö}dinger system reduced to 1D
Nicolas Rougerie, Qiyun Yang
We study a mean-field model for a system of 2D abelian anyons, given by the dynamics of a Schr{ö}dinger matter field coupled to a Chern-Simons gauge field. We derive an effective 1…
Magnetic Thomas-Fermi theory for 2D abelian anyons
Antoine Levitt, Douglas Lundholm, Nicolas Rougerie
Two-dimensional abelian anyons are, in the magnetic gauge picture, represented as fermions coupled to magnetic flux tubes. For the ground state of such a system in a trapping poten…
From bosonic canonical ensembles to non-linear Gibbs measures
van Duong Dinh, Nicolas Rougerie
We study the mean-field limit of the 1D bosonic canonical ensemble in a superharmonic trap. This is the regime with temperature proportional to particle number, both diverging to i…
Gyrokinetic limit of the 2D Hartree equation in a large magnetic field
Denis Périce, Nicolas Rougerie
We study the dynamics of two-dimensional interacting fermions submitted to a homogeneous transverse magnetic field. We consider a large magnetic field regime, with the gap between…
Statistical mechanics of the radial focusing nonlinear Schrödinger equation in general traps
Van Duong Dinh, Nicolas Rougerie, Leonardo Tolomeo +1
In this paper, we investigate the Gibbs measures associated with the focusing nonlinear Schrödinger equation with an anharmonic potential. We establish a dichotomy for normalizabil…
Convergence of states for polaron models in the classical limit
Marco Falconi, Alessandro Olgiati, Nicolas Rougerie
We consider the quasi-classical limit of Nelson-type regularized polaron models describing a particle interacting with a quantized bosonic field. We break translation-invariance by…
Dimensional reduction for a system of 2D anyons
Nicolas Rougerie, Qiyun Yang
Anyons with a statistical phase parameter are a kind of quasi-particles that, for topological reasons, only exist in a 1D or 2D world. We consider the dimensional reduc…
Invariant Gibbs measures for 1D NLS in a trap
Van Duong Dinh, Nicolas Rougerie
We consider the one dimensional cubic nonlinear Schr{ö}dinger equation with trapping potential behaving like |x| s (s > 1) at infinity. We construct Gibbs measures associated to th…
Anyons in a tight wave-guide and the Tonks-Girardeau gas
Nicolas Rougerie, Qiyun Yang
We consider a many-body system of 2D anyons, free quantum particles with general statistics parameter α\in ]0,2[. In the magnetic gauge picture they are described as bosons attache…
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…
On the stability of Laughlin's fractional quantum Hall phase
Nicolas Rougerie
The fractional quantum Hall effect in 2D electron gases submitted to large magnetic fields remains one of the most striking phenomena in condensed matter physics. Historically, the…
Blow-up of 2D attractive Bose-Einstein condensates at the crittical rotational speed
Van Duong Dinh, Dinh-Thi Nguyen, Nicolas Rougerie
We study the ground states of a 2D focusing non-linear Schrödinger equation with rotation and harmonic trapping. When the strength of the interaction approaches a critical value fr…
The classical Jellium and the Laughlin phase
Nicolas Rougerie
I discuss results bearing on a variational problem of a new type, inspired by fractional quantum Hall physics. In the latter context, the main result reviewed herein can be spelled…
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…
The Hartree functional in a double well
Alessandro Olgiati, Nicolas Rougerie
We consider a non-linear Hartree energy for bosonic particles in a symmetric double-well potential. In the limit where the wells are fare apart and the potential barrier is high, w…
Scaling limits of bosonic ground states, from many-body to nonlinear Schr{ö}dinger
Nicolas Rougerie
How and why may an interacting system of many particles be described assuming that all particles are independent and identically distributed ? This question is at least as old as s…
Holomorphic quantum Hall states in higher Landau levels
Nicolas Rougerie, Jakob Yngvason
Eigenstates of the planar magnetic Laplacian with homogeneous magnetic field form degenerate energy bands, the Landau levels. We discuss the unitary correspondence between states i…
A Quantum Impurity Model for Anyons
Enderalp Yakaboylu, Areg Ghazaryan, Douglas Lundholm +3
One of the hallmarks of quantum statistics, tightly entwined with the concept of topological phases of matter, is the prediction of anyons. Although anyons are predicted to be real…