Chaire Aisenstadt

[ English ]

Robert Seiringer (IST Austria)

Séjour: 10-14 septembre 2018

Diaporama de la conférence

SeiringerLes conférences de Robert Seiringer feront partie de l’atelier sur la mécanique quantique à N corps (10–14 septembre) et se tiendront les 10, 12 et 13 septembre.

Biographie

Robert Seiringer a étudié la physique à l'Université de Vienne où il a reçu son doctorat en 2000. Grâce à une bourse Schrödinger, en 2001, il a été à la Princeton University. De 2010 à 2013, il devient professeur à l'Université McGill. Il est maintenant à l'Institute of Science and Technology Austria (IST Austria). Il a reçu une bourse Sloan en 2004, le prix Henri Poincaré en 2009 et la bourse Steacie Memorial en 2012. Il a été un conférencier invité au ICM en 2014. Il est un membre correspondant de l'Austrian Academy of Sciences depuis 2017 et présentement, président de l'IAMP. Robert Seiringer et son groupe de recherche se concentrent sur les systèmes à N corps en mécanique quantique. En particulier, ils s'intéressent aux problèmes en mécanique statistique quantique et en physique de la matière condensée. De tels systèmes affichent une grande variété de phénomènes complexes, et il est d'une importance fondamentale de comprendre les principes sous-jacents aussi profondément et précisément que possible.

 

Conférences

Toutes les conférences auront lieu au Pavillon André-Aisenstadt de l'Université de Montréal.

Le 10 septembre, salle 1140 à 16h

Conférence I. The quantum many-body problem and Bose-Einstein condensation (Conférence s'adressant à un large auditoire scientifique )

Résumé: A detailed understanding of the behaviour of many-particle systems in quantum mechanics poses a formidable challenge to mathematical physics. From the mathematical point of view, it requires a precise spectral analysis of the corresponding Hamiltonian operator. The recent experimental advances in cold-atom physics have led to a renewed interest in studying the quantum many-body problem. The aim of this lecture is to explain part of the progress that was made in the last decade or so. The topics covered include the question of existence of Bose-Einstein condensation, superfluidity and quantised vortices in systems in rotating traps, as well as recent investigations on the structure of the excitation spectrum for weakly interacting fluids. We will describe the mathematics involved in understanding these phenomena, starting from the underlying many-body Schrödinger equation.

Le 12 septembre salle 6254 à 16h

Conférence II. Bose-Einstein condensation in dilute, trapped gases at positive temperature

Résumé: We consider an interacting, dilute Bose gas trapped in a harmonic potential at positive temperature, in a combination of a thermodynamic and a Gross-Pitaevskii (GP) limit. We prove that the difference between the canonical free energy of the interacting gas and the one of the noninteracting system can be obtained by minimizing the GP energy functional. We also prove Bose-Einstein condensation, in the sense that  the one-particle density matrix of the interacting Gibbs state is to leading order given by that of the noninteracting gas but with the free condensate wavefunction replaced by the GP minimizer. (Joint work with A. Deuchert and J. Yngvason)

Le 13 septembre salle 6254 à 16h

Conférence III. Quantum many-body systems with point interactions

Résumé: We investigate the stability of quantum many-body systems with point interactions. In particular, we present a proof that a system of N fermions interacting with an additional particle via point interactions is stable if the ratio of the mass of the additional particle to the one of the fermions is larger than some critical value. For this impurity problem, we also show that the ground state energy of the system at given non-zero mean density differs from the one of the ideal gas by a term depending only on the density and the scattering length of the interactions, independently of N.  While the general problem with more than one impurity remains open, we can show stability for the simplest such system, the one consisting of two fermions interacting with two (fermionic) impurities. (Joint work with T. Moser)