The seminars take place on Wednesday afternoon, usually at 14:30 Italian time.
November 6th, 2024
Volker Bach (Technische Universität Braunschweig)
An overview on nonrelativistic QED
The talk will survey a number of results concerning the mathematical foundation of nonrelativistic quantum electrodynamics.
December 18th, 2024
David Pérez García (Universidad Complutense Madrid)
Spectral gaps in many body quantum systems
How does the spectral gap of a quantum many body system scale with the system size? This turns out to be a very relevant question both in condensed matter physics and in quantum computing. However, there are very few available techniques to give bounds of that scaling. In the first part of this talk, we will review recent results which explain why: it is undecidable to know if the spectral gap will vanish or not with the system size. In the second part, we will review complementary results which show that, despite this general impossibility result, one can still prove spectral gap estimates in a rather wide family of systems. As a consequence, one obtains new bounds on the lifetime of quantum memories.
January 15th, 2025
Robert Seiringer (Institute of Science and Technology Austria)
Spectral analysis of polaron models in the strong coupling limit
The Fröhlich polaron and related models of quantum field theory have played a prominent role in mathematical physics over several decades. In this talk, we shall explain recent bounds on the quantum corrections to the (classical) Pekar approximation of the ground state energy of the Fröhlich polaron model in the strong coupling limit, and their consequence on the existence of excited states and the polaron's effective mass.
March 12th, 2025
Andrea R. Nahmod (University of Massachusetts Amherst)
CANCELLED
April 9th, 2025
Rafael D. Benguria (Pontificia Universidad Católica de Chile)
Bound on the Excess Charge of Generalized Thomas-Fermi-Weizsäcker Functionals
We bound the number of electrons Q that an atom can bind in excess of neutrality for density functionals generalizing the classical Thomas-Fermi-Weizsäcker functional: instead of the classical power 5/3 more general powers p are considered. For 3/2 < p < 2 we prove the excess charge conjecture, i.e., that Q is uniformly bounded in the atomic number Z. The case p = 3/2 is critical: the behavior changes from a uniform bound in Z to a linear bound at the critical coupling 4 √ π of the nonlinear term. We also improve the linear bound for all p ≥ 6/5.
This is joint work with Heinz Siedentop, LMU, Munich.
May 14th, 2025
Nicola Pinamonti (Università degli Studi di Genova)
Interacting regularised scalar quantum field theories: convergence of the S-matrix
We discuss the construction of self-interacting scalar quantum field theories on d-dimensional Minkowski spacetime, focusing on a class of interaction Lagrangians given by suitable functions of the scalar field. Using perturbation theory, we express interacting field observables as formal power series expansions over the free theory. Central to this construction is the time-ordered exponential of the interaction Lagrangian—the S-matrix—which itself is a power series in the coupling constant.
We introduce a regularization procedure that renders the S-matrix convergent to well-defined unitary operators. This regularization involves two parameters: one controlling the suppression of high-frequency modes in the propagators, and another regulating large field contributions in the interaction Lagrangian. We analyze the removal of these regularization parameters in lower-dimensional theories and for specific interaction Lagrangians.
In particular, we show that for a φ4 theory in three spacetime dimensions, form sequences of regularized S-matrices obtained scaling the regularization parameters to zero we can extract convergent subsequences in the weak-* topology. The asymptotic expansions of all the possible limit points of the extracted subsequences agree and match the predictions of perturbation theory. We also outline how these results extend to the four-dimensional case, where similar behavior is observed.
