Maths-Physics meeting on superfluidity, solitons and dissipation
📆 January 11th 2022
The meeting is maintained, no drinks or food….
📍Laboratoire de Physique, École normale supérieure, 24 rue Lhomond, Paris, Room L367
Organization : Amandine Aftalion and Frédéric Chevy
Meeting funded by the CNRS Prime project TraDisQ1D – Transport et Dissipation dans les systèmes quantiques unidimensionnels
Program
8h45 : Welcome, no coffee
9h00-9h35 : Alberto Bramati – « Quantum Fluids of Light »
Slides here – Video here
9h35-9h55 : questions and discussions
10h00-10h35 : Vincent Hakim – « Critical velocity and transition in the flow of a one-dimensional resonantly-driven polariton fluid past an obstacle »
10h35-10h55 : questions and discussions
11h00-11h35 : Étienne Sandier – « Solitons and solitonic vortices in an infinite stripe from a variational viewpoint »
Video here
11h35-11h55 : questions and discussions
12h00-12h35 : Jérôme Beugnon – « Deterministic preparation of a two-dimensional soliton in a scale-invariant Bose gas »
Slides of the talk here – Video here
12h35-12h55 : questions and discussions
14h15-14h50 : Philippe Gravejat – « Travelling waves for the nonlinear Schrödinger equation »
Slides of the talk here – Video here
14h50-15h10 : questions and discussions
Abstracts
Jérôme Beugnon (Laboratoire Kastler Brossel, Sorbonne Université, Ecole Normale Supérieure, CNRS, Paris) – « Deterministic preparation of a two-dimensional soliton in a scale-invariant Bose gas »
Abstract: Solitons are usually unstable in dimensions higher than one. Here, using an ultracold planar Bose gas, we prepare and study a marginally unstable soliton associated to the 2D non-linear Schrodinger equation with cubic non-linearity: the so-called Townes soliton. We show that, quite surprisingly, this soliton appears only for a specific atom number and we prove its scale-invariance. We also extend the discussion beyond the cubic non-linearity case and explore the associated excitation modes.
Alberto Bramati (Laboratoire Kastler Brossel, Sorbonne Université, Ecole Normale Supérieure, CNRS, Paris) – « Quantum Fluids of Light ».
Abstract: Photons confined in optical cavities or propagating in paraxial geometries acquire an effective mass and behave like matter particles. Moreover an effective photon-photon interaction can be engineered when the photons propagate in a nonlinear medium, resulting in a collective fluid-like behavior of light. A few years ago, the superfluid behavior of light was observed in such systems, the so called quantum fluids of light [1]. This lecture will show how these properties have been studied and how they can be used to simulate astrophysical systems, such as Black Holes.
Reference : [1] I. Carusotto and C. Ciuti, « Quantum Fluids of Light », Rev. Mod. Phys. 85, 299 (2013).
Philippe Gravejat (CY Cergy Paris Université) – « Travelling waves for the nonlinear Schrödinger equation ».
Abstract : The goal of this talk is to describe several mathematical results concerning the travelling waves solutions for the nonlinear Schrödinger equation with non zero conditions at infinity. A special focus will be put on their construction and their stability properties.
Vincent Hakim (Laboratoire de Physique de l’ENS, Paris) – « Critical velocity and transition in the flow of a one-dimensional resonantly-driven polariton fluid past an obstacle ».
Abstract: The onset of dissipation at a critical velocity in a superfluid has been the subject of numerous experimental and theoretical works since the work of Landau. Following the recent experimental study of a polariton field flowing past an obstacle, we theoretically analyze the analogous phenomenon for a « quantum fluid of light » that is both driven and dissipative, and exhibit bistability. We show that while a transition at a critical velocity still exists, its character is very different from the classic Landau transition. Work performed in collaboration with A. Aftalion and S. Pigeon.
Étienne Sandier (Université Paris Est Créteil Val de Marne) – « Solitons and solitonic vortices in an infinite stripe from a variational viewpoint ».
Abstract: Recent experiments and numerical investigations have focused on objects coined as solitonic vortices. I will present a few mathematical results obtained with A.Aftalion which aim at characterizing them in variational terms, and comparing them to the solitons, taking as a parameter the width of the stripe.
