Riccardo Adami (Politecnico di Torino)
Title: A mathematical model for the EPR phenomenon.
Abstract. We consider a couple of quantum non-identical particles that are constrained to one spatial dimension and are initially entangled in the position and momentum variables. They do not interact with each other while one of them, i.e. particle 1, interacts with a spin locate at a fixed position. We introduce a scaling that involves the strength and the width of the interaction, the energy of the spin, and the Planck’s constant. We show that, at the first order in the small scaling parameter, the spin flip is correlated with the motion of particle 2, that does not interact with it. This is a version of the effect theoretically foreseen by Einstein, Podoslki and Rosen in their famous paper of 1935. The research project is in collaboration with L. Barletti (Florence) and A. Teta (Rome).
Luca Fresta (Universität Bonn)
Title: Dynamics of extended Fermi gases at high density
Abstract: In my talk, I will discuss the quantum evolution of many-body Fermi gases confined in arbitrarily large domains, focusing on a high-density/semiclassical scaling regime. I will show that, as the density approaches infinity, the many-body evolution of the reduced one-particle density matrix converges in trace norm to the solution of the Hartree equation, with convergence rate depending on the density only. The result holds for short macroscopic times for non-relativistic particles, but extends to arbitrary times in the case of pseudo-relativistic dispersion. In the latter case, I will also show that the convergence holds in the stronger sense of expectation of local observables.
Based on joint works with Marcello Porta and Benjamin Schlein.
Asbjørn Bækgaard Lauritsen (IST Austria)
Title: Universalities in BCS Theory
Abstract: In nature one finds superconductors of varying critical temperatures and energy gaps. For weak superconductors, where the critical temperature is small, a universal phenomenon occurs: The ratio of the energy gap and critical temperature is a universal value, independent of the specific superconductor. I will present recent work on such universal phenomena in the BCS theory of superconductivity.
Joint work with Joscha Henheik and Barbara Roos.
Mathieu Lewin (Université Paris Dauphine)
Title: The electronic ground state energy is not always convex in the number of electrons
Abstract: A famous conjecture states that, for atoms and molecules, the electronic ground state energy is convex in the number of electrons. We give the first counter-example to this conjecture, for a molecule containing nuclei with small fractional charges. The problem is still open for real nuclei with integer charges. The counter-example is based on optimal transport methods.
Phan Thành Nam (LMU Munich)
Title: A quantum variance inequality and its application to the Bose gas
Abstract: I will discuss a general inequality that allows for controlling the variance of a Gibbs state through first moment estimates of suitably perturbed states. This result is derived from Stahl’s theorem on Laplace transforms for matrix functions and provides a helpful tool for understanding the behavior of the interacting Bose gas at the critical temperature of Bose-Einstein condensation. This is recent joint work with Andreas Deuchert and Marcin Napiórkowski, inspired by a previous result with Mathieu Lewin and Nicolas Rougerie.
Alessandro Olgiati (Politecnico di Milano)
Title: Wu’s correction to the ground state energy of a Bose gas in the Gross-Pitaevskii regime
Abstract: We consider a Bose gas trapped on the 3d unit torus in the Gross-Pitaevskii (GP) regime and compute the ground state energy up to an error which vanishes faster than N ⁻¹ log N as N → ∞ . Our result is compatible with a prediction formulated by Wu in the 1950s for the correction to the Lee-Huang-Yang formula in the thermodynamic limit. The proof involves a renormalization of the Hamiltonian through conjugation with unitary operators that implement two-body and three-body correlations. We need in particular a non-trivial improvement of the structure of three-body correlations compared to earlier results.
Joint work with Cristina Caraci (University of Geneva), Diane Saint Aubin (University of Zurich), and Benjamin Schlein (University of Zurich).
Andrew Rout (Université de Rennes)
Title: Gibbs measures and KMS states for the focusing nonlinear Schrödinger equation
Abstract: Gibbs measures are an important object in the study of low regularity well posedness of nonlinear Hamiltonian PDEs. On the other hand, the KMS condition is a method of singling out equilibrium states in a dynamical system. In this talk, I discuss some recent results on the relationship between KMS states and Gibbs measures for the focusing nonlinear Schrödinger equation.
Based on work with Zied Ammari and Vedran Sohinger.
Benjamin Schlein (Universität Zürich)
TBA
Robert Seiringer (IST Austria)
TBA
Stefan Teufel (Universität Tübingen)
TBA