Mathematical Challenges in Quantum Mechanics - Online Seminars

Nov 8, 2023, 9:00 AM → May 16, 2024, 1:00 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 14:15 Italian time, on a monthly basis. The schedule of the upcoming seminars is:     
 

• November 8, 2023 
  Nilanjana Datta (University of Cambridge)
   
• December 13, 2023 
  Marco Merkli (Memorial University of Newfoundland)
   
• January 10, 2023 
  Hal Tasaki (Gakushin University)

 

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. 

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 MCQM_Seminar_Cances_2022-12-14.pdf

Wednesday, November 8

1 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.

2 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, December 13

3 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.

4 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, January 10

5 MCQM PhD Lecture: Chris Bourne (Nagoya University)

Title: TBA

Abstract: TBA

6 MCQM Seminar: Hal Tasaki (Gakushuin University)

Title: TBA

Abstract: TBA