Mathematical Challenges in Quantum Mechanics - Online Seminars

8 Nov 2023, 09:00 → 31 May 2024, 23:00 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 14:15 Italian time, on a monthly basis. The schedule of the 2024 seminar series is:       
 

• November 8, 2023   
  Nilanjana Datta (University of Cambridge)  
   
• December 13, 2023   
  Marco Merkli (Memorial University of Newfoundland)  
   
• January 10, 2024   
  Hal Tasaki (Gakushin University) 
   
• February 21, 2024 
  Fumio Hiroshima (Kyushu University) 
   
• March 13, 2024 
  Soeren Fournais (University of Copenhagen) 
   
• April 24, 2024
  Alessandro Teta (Sapienza, Università di Roma)
   
• May 29, 2024
  Simone Warzel (TMU)
   

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 will be 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 (LMU)     
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 Seminars 2022/23 hiro.pdf MCQM_Seminar_Cances_2022-12-14.pdf

Wednesday, 8 November

11:30 → 12:30 MCQM PhD Lecture: Angela Capel Cuevas

Title: Quantum entropy and trace inequalities

Abstract: In this talk, I will give an elementary introduction to the subject of quantum entropies and trace inequalities, with a special focus on results that are relevant to quantum information theory. First, we will discuss various different notions of quantum entropies that extend those of classical entropies, and we will show several of their fundamental properties, in particular under the application of quantum channels. We will put a special focus on those properties that differ from their classical counterparts. Next, we will describe some contexts within quantum Shannon theory in which the use of quantum entropies is fundamental, such as for quantum hypothesis testing or to estimate quantum channel capacities.

14:15 → 15:15 MCQM Seminar: Nilanjana Datta

Title: Universal proofs of entropic continuity bounds via majorization flow

Abstract: We employ majorization theory to obtain a powerful tool for deriving simple and universal proofs of continuity bounds for various entropies which are relevant in information theory. In obtaining this, we first state a more general result which may be of independent interest: a necessary and sufficient condition under which a state maximizes a concave, continuous, Gateaux-differentiable function in an epsilon-ball in trace distance. Examples of such a function include the von Neumann entropy, Renyi entropies, and the conditional entropy. In particular, by introducing a notion of majorization flow, we prove that the alpha-Rényi entropy is Lipschitz continuous, for alpha greater than 1, thus resolving an open problem and providing a substantial improvement over previously known bounds. This is joint work with Eric Hanson.

Wednesday, 13 December

11:30 → 12:30 MCQM PhD Lecture: Stefano Marcantoni (Université Côte d'Azur, LJAD)

Title: Introduction to the theory of open quantum systems

Abstract: In this lecture, I will introduce the framework commonly used to describe the dynamics of open quantum systems. This is based on completely positive dynamical maps and markovian master equations in GKSL (Gorini-Kossakowski-Sudarshan-Lindblad) form. I will discuss the general structure of the latter for an N-level system and present some simple examples. Among them, I will focus on the so-called "Davies generator" induced by the interaction with a thermal Bose field, whose rigorous derivation was originally given by Davies in the van Hove scaling limit and has been recently improved by Merkli uniformly in time. Finally, I will also mention a few directions of current research and point to some relevant literature.

14:15 → 15:15 MCQM Seminar: Marco Merkli (Memorial University of Newfoundland)

Title: Open quantum system dynamics and metastability

Abstract: We consider the paradigmatic model of an open quantum system, an N-level system in contact with a thermal Bose field (reservoir) and study the evolution of the system-reservoir complex. We show that under suitable conditions the ubiquitous Born and Markov approximations -- that is, the markovian master equation -- can be proven to hold on all time scales. In case there is correlation between the system and the reservoir in the initial state, our results show that the markovian master equation is still valid, that the correlations decay in time and that after the decay, the Born approximation becomes valid. We will explain the results first and then present the main ideas of the mathematical methods used to show them. We will focus in particular on the dynamical resonance theory, which describes the effective dynamics of the N-level system in terms of metastable states (slowly decaying in time) arising from perturbation of unstable bound states of the non-interacting system-reservoir complex.

Wednesday, 10 January

11:30 → 12:30 MCQM PhD Lecture: Ian Jauslin (Rutgers University)

Title: Typicality in Statistical Mechanics and the arrow of time

Abstract: In this lecture, I will give a brief overview of the foundations of statistical mechanics, with a focus on typicality in classical settings, and hint at generalizations to the quantum setting. I will also discuss open problems in equilibrium statistical mechanics.

14:15 → 15:15 MCQM Seminar: Hal Tasaki (Gakushuin University)

Title: What is thermal equilibrium and how do we get there? --- Typicality and thermalization in isolated macroscopic quantum systems

Abstract: I discuss the foundation of equilibrium statistical mechanics based on the quantum mechanics of isolated macroscopic systems. After clarifying what the equilibrium statistical mechanics is all about, I will present the modern understanding that thermal equilibrium should be regarded as a property (or a collection of properties) that an overwhelming majority of legitimate physical states share. This typicality picture is supported by firm mathematical considerations and (in my opinion) now has been accepted by a majority of experts. I will then turn to the much more difficult (and largely unsolved) question of thermalization, i.e., the approach to thermal equilibrium by means of the quantum-mechanical unitary time evolution. I will discuss general scenarios of thermalization based on the ETH (energy eigenstate thermalization hypothesis) or the hypothesis of a large effective dimension. I will finally discuss my recent result with Naoto Shiraishi on a fully rigorous example of thermalization in (unfortunately) a free fermion chain. The main part of the talk is based on the work of various authors. The references can be found in the following two papers of ours. https://arxiv.org/abs/1507.06479 https://arxiv.org/abs/2310.18880.

Wednesday, 21 February

11:30 → 12:30 MCQM PhD Lecture: David Mitrouskas (ISTA Austria)

TBA

14:15 → 15:15 MCQM Seminar: Fumio Hiroshima (Kyushu University)

TBA

Wednesday, 13 March

11:30 → 12:30 MCQM PhD Lecture: Lea Boßmann (Johannes Gutenberg Universität Mainz)

Title: A brief introduction to the interacting Bose gas

Abstract: Since the first experimental realization of a Bose-Einstein condensate in 1995, the physical and mathematical analysis of the Bose gas has become a very active field of research. In this lecture, I will give a short introduction to the topic from a mathematical perspective. I will focus on spectral properties of interacting Bose gases, in particular on their ground state energy and low-energy excitation spectrum.

14:15 → 15:15 MCQM Seminar: Søren Fournais (University of Copenhagen)

Title: The dilute Bose gas at positive temperature

Abstract: In this talk, I will report on recent work concerning the free energy of the dilute Bose gas in the case of strong interactions. In particular hard sphere potentials are allowed. When combining recent progress on Neumann bracketing for this many-body problem with the “completion-of-the-square” approach used previously on the hard-sphere case at zero-temperature, one obtains a short and simple proof of a lower bound for the free energy in the dilute limit up to temperatures of magnitude ρ a. Here ρ is the particle density and a is the scattering length of the interaction. This is joint work with T. Girardot, L. Junge, L. Morian, M. Olivieri, and A. Triay.

Wednesday, 24 April

11:30 → 12:30 MCQM PhD Lecture: Jonas Lampart (Université de Bourgogne)

Title: Contact interactions and generalised boundary conditions

Abstract: Hamiltonians for a particle interacting with a point-like obstacle can be constructed as self-adjoint extensions of the Laplacian restricted to functions vanishing near the obstacle. These are characterised by a generalised boundary condition. They can be embedded into a larger family of Hamiltonians that also allow the particle to be absorbed or emitted at the obstacle.
After explaining these elementary constructions in detail, I will outline some generalisations to non-relativistic models in quantum field theory.

14:15 → 15:15 MCQM Seminar: Alessandro Teta (Sapienza Università di Roma)

Title: Many-particle systems with contact interactions

Abstract: Quantum Hamiltonians with contact (or zero-range) interactions are useful models to analyze the behaviour of quantum systems at low energy in different contexts. In this talk we discuss recent mathematical results on the construction of such Hamiltonians for a system of $N \geq 3$ interacting bosons in dimension three as self-adjoint and lower bounded operators in the appropriate Hilbert space. We will also show the connection with a previous result obtained by Albeverio, Hoegh-Krohn and Streit in 1977 and we will discuss possible applications to the Efimov effect.
The talk is based on a series of works in collaboration with G. Basti, C. Cacciapuoti, D. Ferretti, R. Figari, D. Finco and H. Saberbaghi.

Wednesday, 29 May

11:30 → 12:30 MCQM PhD Lecture: Christian Brennecke (Universität Bonn)

Title and abstract: TBA

14:15 → 15:15 MCQM Seminar: Simone Warzel (Technische Universität München)

Title and abstract: TBA