71 citations · 752 across the 67 of their papers we have counts for
19 papers · 1 filter
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…
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…
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…
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…
On two properties of the Fisher information
Nicolas Rougerie
Alternative proofs for the superadditivity and the affinity (in the large system limit) of the usual and some fractional Fisher informations of a probability density of many variab…
Improved stability for 2D attractive Bose gases
Phan Thành Nam, Nicolas Rougerie
We study the ground-state energy of N attractive bosons in the plane. The interaction is scaled for the gas to be dilute, so that the corresponding mean-field problem is a local no…
Non linear Schr{ö}dinger limit of bosonic ground states, again
Nicolas Rougerie
I review an information-theoretic variant of the quantum de Finetti theorem due to Brand{ã}o and Harrow and discuss its applications to the topic of bosonic mean-field limits. This…
Classical field theory limit of many-body quantum Gibbs states in 2D and 3D
Mathieu Lewin, Phan Thành Nam, Nicolas Rougerie
We provide a rigorous derivation of nonlinear Gibbs measures in two and three space dimensions, starting from many-body quantum systems in thermal equilibrium. More precisely, we p…
Blow-up profile of rotating 2D focusing Bose gases
Mathieu Lewin, Phan Thành Nam, Nicolas Rougerie
We consider the Gross-Pitaevskii equation describing an attractive Bose gas trapped to a quasi 2D layer by means of a purely harmonic potential, and which rotates at a fixed speed…