Mathematical Challenges in Quantum Mechanics - Online Seminars

Nov 1, 2024, 9:00 AM → May 31, 2025, 11:00 PM Europe/Rome

Online

The series of online seminars Mathematical Challenges in Quantum Mechanics (MCQM) focuses on current topics of mathematical physics, with special attention to the mathematical aspects of quantum mechanics. It aims to bring together the Italian community working on mathematical methods for quantum theory.      

The seminars take place on Wednesday afternoon, usually at 14:30 Italian time, on a monthly basis. The schedule for the 2024/25 seminar series is as follows:       
 

• November 6, 2024   
  Volker Bach (Technische Universität Braunschweig)  
   
• December 18, 2024   
  David Pérez García (Universidad Complutense Madrid)  
   
• January 15, 2025   
  Robert Seiringer (Institute of Science and Technology Austria) 
   
• February 9-14, 2025 — MCQM goes live!
  School and Workshop Mathematical Challenges in Quantum Mechanics (GSSI, L'Aquila, Italy) 
   
• March 12, 2025 
  Andrea Nahmod (University of Massachusetts Amherst) CANCELLED
   
• April 9, 2025
  Rafael Benguria (Pontificia Universidad Católica de Chile)
   
• May 2025
  TBA
   

Each seminar will be accompanied by a lecture addressed to PhD students and young researchers, aimed at introducing the broad topic of the seminar and presenting some perspectives of the open problems and mathematical challenges in the field. The lecture is usually held on the same day of the seminar, at 11.30 Italian time.

Titles and abstracts of the MCQM Seminars and PhD lectures are available at this page and this page respectively. To receive the zoom link to attend the seminars and/or the PhD lectures please register here. 

The online seminars are part of a long-running series of events organized over the years by the Italian community working on mathematical methods for quantum physics, including the following School and Workshops: 

MCQM - Mathematical Challenges in Quantum Mechanics  
MCQM22 - Como, June 13-18, 2022 
MCQM18 - Rome, February 19-24, 2018  
MCQM16 - Bressanone, February 8-13, 2016

Organizing committee

Serena Cenatiempo (GSSI)     
Marco Falconi (PoliMi)     
Emanuela L. Giacomelli (UniMI)     
Domenico Monaco (Sapienza)     
Marco Olivieri (Copenhagen)     

 

MCQM PhD Lectures 2022/23

• MCQM PhD Lecture_Boni_Quantum graphs_2023-05-17.pdf
• MCQM_PhDLecture_Gontier_2022-12-14.pdf
• MCQM_PhDLecture_Koenig_2022-11-09.pdf
• MCQM_PhDLecture_Shapiro_2023-01-10.pdf

MCQM PhD Lectures 2023/24 TalkEntropies_Capel_highlighted.pdf TalkEntropies_Capel.pdf

MCQM PhD Lectures 2024/25

• 2024-01-15_Hinrichs.pdf
• 2024-11-06_Alvarez_bibliography.pdf
• 2024-12-18_Lucia_slides.pdf

MCQM Seminars 2022/23 hiro.pdf MCQM_Seminar_Cances_2022-12-14.pdf

Wednesday, November 6

1 MCQM PhD Lecture: Benjamin Alvarez

Title: An introduction to non relativistic QED

Abstract: This talk is dedicated to presenting the fundamental notions to adress non relativistic QED models. The general framework of quantum field theory will be presented together with the Hamiltonian of non relativistic QED. In addition, we aim to give a taste of important works that have been done in the field together with some open problems.

2 MCQM Seminar: Volker Bach

Title: TBA

Abstract: TBA

Wednesday, December 18

3 MCQM PhD Lecture: Angelo Lucia

Title: Locality and spectral gaps in quantum spin systems

Abstract: In this lecture, I will give a brief introduction to the mathematical framework used to describe quantum spin systems on lattices. The main goal will be to connect the study of models defined over finite volumes to an idealized infinite volume limit called the thermodynamic limit. A key role will be played by locality estimates known as Lieb-Robinson bounds. I will then focus on the spectral gap of the model, the difference between the two lowest energy levels, and I will explain how it is related to the problem of phase classification of quantum phases of matter.

4 MCQM Seminar: David Pérez García

Title: Spectral gaps in many body quantum systems

Abstract: 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.

Wednesday, January 15

5 MCQM PhD Lecture: Benjamin Hinrichs

Title: An Invitation to Path Measure Methods for Polaron Models

Abstract: This talk gives an introduction to the connection between the Hamiltonian formulation of quantum mechanics and its probabilistic counterpart. We first discuss this in terms of Feynman-Kac formulas for Schrödinger operators together with some applications. Then, we move to their analogues for polaron models, i.e., models of quantum particles linearly coupled to a quantum field. We also sketch how the named applications extend to the polaron, e.g., when studying ground states or the effective mass.

6 MCQM Seminar: Robert Seiringer

Title: Spectral analysis of polaron models in the strong coupling limit

Abstract: 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.

Wednesday, March 12

7 MCQM PhD Lecture: Andrew Rout

Title: A (brief) introduction to Gibbs measures for the nonlinear Schrödinger equation

Abstract: In this talk I will give an introduction to Gibbs measures for the nonlinear Schrödinger equation. The construction of global solutions to dispersive PDEs usually relies on the conservation of quantities like the energy and the mass. For lower regularity functions, these quantities are infinite, so cannot be used. Instead one introduces an invariant measure, which can act as a substitute for the conserved quantities.
I give the heuristic ideas for the construction the Gibbs measure, and also sketch the details of the rigorous construction. I will also discuss how to use the Gibbs measure to construct global solutions to the nonlinear Schrödinger equation.

Wednesday, April 9

8 MCQM Seminar: Rafael Benguria

Title: Bound on the Excess Charge of Generalized Thomas-Fermi-Weizsäcker functionals

Abstract: 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.