Mathematical Challenges in Quantum Mechanics - Online Seminars
from
Wednesday, 8 November 2023 (09:00)
to
Friday, 31 May 2024 (23:00)
Monday, 6 November 2023
Tuesday, 7 November 2023
Wednesday, 8 November 2023
11:30
MCQM PhD Lecture: Angela Capel Cuevas
MCQM PhD Lecture: Angela Capel Cuevas
11:30 - 12:30
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
MCQM Seminar: Nilanjana Datta
MCQM Seminar: Nilanjana Datta
14:15 - 15:15
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.
Thursday, 9 November 2023
Friday, 10 November 2023
Saturday, 11 November 2023
Sunday, 12 November 2023
Monday, 13 November 2023
Tuesday, 14 November 2023
Wednesday, 15 November 2023
Thursday, 16 November 2023
Friday, 17 November 2023
Saturday, 18 November 2023
Sunday, 19 November 2023
Monday, 20 November 2023
Tuesday, 21 November 2023
Wednesday, 22 November 2023
Thursday, 23 November 2023
Friday, 24 November 2023
Saturday, 25 November 2023
Sunday, 26 November 2023
Monday, 27 November 2023
Tuesday, 28 November 2023
Wednesday, 29 November 2023
Thursday, 30 November 2023
Friday, 1 December 2023
Saturday, 2 December 2023
Sunday, 3 December 2023
Monday, 4 December 2023
Tuesday, 5 December 2023
Wednesday, 6 December 2023
Thursday, 7 December 2023
Friday, 8 December 2023
Saturday, 9 December 2023
Sunday, 10 December 2023
Monday, 11 December 2023
Tuesday, 12 December 2023
Wednesday, 13 December 2023
11:30
MCQM PhD Lecture: Stefano Marcantoni (Université Côte d'Azur, LJAD)
MCQM PhD Lecture: Stefano Marcantoni (Université Côte d'Azur, LJAD)
11:30 - 12:30
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
MCQM Seminar: Marco Merkli (Memorial University of Newfoundland)
MCQM Seminar: Marco Merkli (Memorial University of Newfoundland)
14:15 - 15:15
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.
Thursday, 14 December 2023
Friday, 15 December 2023
Saturday, 16 December 2023
Sunday, 17 December 2023
Monday, 18 December 2023
Tuesday, 19 December 2023
Wednesday, 20 December 2023
Thursday, 21 December 2023
Friday, 22 December 2023
Saturday, 23 December 2023
Sunday, 24 December 2023
Monday, 25 December 2023
Tuesday, 26 December 2023
Wednesday, 27 December 2023
Thursday, 28 December 2023
Friday, 29 December 2023
Saturday, 30 December 2023
Sunday, 31 December 2023
Monday, 1 January 2024
Tuesday, 2 January 2024
Wednesday, 3 January 2024
Thursday, 4 January 2024
Friday, 5 January 2024
Saturday, 6 January 2024
Sunday, 7 January 2024
Monday, 8 January 2024
Tuesday, 9 January 2024
Wednesday, 10 January 2024
11:30
MCQM PhD Lecture: Ian Jauslin (Rutgers University)
MCQM PhD Lecture: Ian Jauslin (Rutgers University)
11:30 - 12:30
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
MCQM Seminar: Hal Tasaki (Gakushuin University)
MCQM Seminar: Hal Tasaki (Gakushuin University)
14:15 - 15:15
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.
Thursday, 11 January 2024
Friday, 12 January 2024
Saturday, 13 January 2024
Sunday, 14 January 2024
Monday, 15 January 2024
Tuesday, 16 January 2024
Wednesday, 17 January 2024
Thursday, 18 January 2024
Friday, 19 January 2024
Saturday, 20 January 2024
Sunday, 21 January 2024
Monday, 22 January 2024
Tuesday, 23 January 2024
Wednesday, 24 January 2024
Thursday, 25 January 2024
Friday, 26 January 2024
Saturday, 27 January 2024
Sunday, 28 January 2024
Monday, 29 January 2024
Tuesday, 30 January 2024
Wednesday, 31 January 2024
Thursday, 1 February 2024
Friday, 2 February 2024
Saturday, 3 February 2024
Sunday, 4 February 2024
Monday, 5 February 2024
Tuesday, 6 February 2024
Wednesday, 7 February 2024
Thursday, 8 February 2024
Friday, 9 February 2024
Saturday, 10 February 2024
Sunday, 11 February 2024
Monday, 12 February 2024
Tuesday, 13 February 2024
Wednesday, 14 February 2024
Thursday, 15 February 2024
Friday, 16 February 2024
Saturday, 17 February 2024
Sunday, 18 February 2024
Monday, 19 February 2024
Tuesday, 20 February 2024
Wednesday, 21 February 2024
11:30
MCQM PhD Lecture: David Mitrouskas (ISTA Austria)
MCQM PhD Lecture: David Mitrouskas (ISTA Austria)
11:30 - 12:30
TBA
14:15
MCQM Seminar: Fumio Hiroshima (Kyushu University)
MCQM Seminar: Fumio Hiroshima (Kyushu University)
14:15 - 15:15
TBA
Thursday, 22 February 2024
Friday, 23 February 2024
Saturday, 24 February 2024
Sunday, 25 February 2024
Monday, 26 February 2024
Tuesday, 27 February 2024
Wednesday, 28 February 2024
Thursday, 29 February 2024
Friday, 1 March 2024
Saturday, 2 March 2024
Sunday, 3 March 2024
Monday, 4 March 2024
Tuesday, 5 March 2024
Wednesday, 6 March 2024
Thursday, 7 March 2024
Friday, 8 March 2024
Saturday, 9 March 2024
Sunday, 10 March 2024
Monday, 11 March 2024
Tuesday, 12 March 2024
Wednesday, 13 March 2024
11:30
MCQM PhD Lecture: Lea Boßmann (Johannes Gutenberg Universität Mainz)
MCQM PhD Lecture: Lea Boßmann (Johannes Gutenberg Universität Mainz)
11:30 - 12:30
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
MCQM Seminar: Søren Fournais (University of Copenhagen)
MCQM Seminar: Søren Fournais (University of Copenhagen)
14:15 - 15:15
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.
Thursday, 14 March 2024
Friday, 15 March 2024
Saturday, 16 March 2024
Sunday, 17 March 2024
Monday, 18 March 2024
Tuesday, 19 March 2024
Wednesday, 20 March 2024
Thursday, 21 March 2024
Friday, 22 March 2024
Saturday, 23 March 2024
Sunday, 24 March 2024
Monday, 25 March 2024
Tuesday, 26 March 2024
Wednesday, 27 March 2024
Thursday, 28 March 2024
Friday, 29 March 2024
Saturday, 30 March 2024
Sunday, 31 March 2024
Monday, 1 April 2024
Tuesday, 2 April 2024
Wednesday, 3 April 2024
Thursday, 4 April 2024
Friday, 5 April 2024
Saturday, 6 April 2024
Sunday, 7 April 2024
Monday, 8 April 2024
Tuesday, 9 April 2024
Wednesday, 10 April 2024
Thursday, 11 April 2024
Friday, 12 April 2024
Saturday, 13 April 2024
Sunday, 14 April 2024
Monday, 15 April 2024
Tuesday, 16 April 2024
Wednesday, 17 April 2024
Thursday, 18 April 2024
Friday, 19 April 2024
Saturday, 20 April 2024
Sunday, 21 April 2024
Monday, 22 April 2024
Tuesday, 23 April 2024
Wednesday, 24 April 2024
11:30
MCQM PhD Lecture: Jonas Lampart (Université de Bourgogne)
MCQM PhD Lecture: Jonas Lampart (Université de Bourgogne)
11:30 - 12:30
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
MCQM Seminar: Alessandro Teta (Sapienza Università di Roma)
MCQM Seminar: Alessandro Teta (Sapienza Università di Roma)
14:15 - 15:15
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.
Thursday, 25 April 2024
Friday, 26 April 2024
Saturday, 27 April 2024
Sunday, 28 April 2024
Monday, 29 April 2024
Tuesday, 30 April 2024
Wednesday, 1 May 2024
Thursday, 2 May 2024
Friday, 3 May 2024
Saturday, 4 May 2024
Sunday, 5 May 2024
Monday, 6 May 2024
Tuesday, 7 May 2024
Wednesday, 8 May 2024
Thursday, 9 May 2024
Friday, 10 May 2024
Saturday, 11 May 2024
Sunday, 12 May 2024
Monday, 13 May 2024
Tuesday, 14 May 2024
Wednesday, 15 May 2024
Thursday, 16 May 2024
Friday, 17 May 2024
Saturday, 18 May 2024
Sunday, 19 May 2024
Monday, 20 May 2024
Tuesday, 21 May 2024
Wednesday, 22 May 2024
Thursday, 23 May 2024
Friday, 24 May 2024
Saturday, 25 May 2024
Sunday, 26 May 2024
Monday, 27 May 2024
Tuesday, 28 May 2024
Wednesday, 29 May 2024
11:30
MCQM PhD Lecture: Christian Brennecke (Universität Bonn)
MCQM PhD Lecture: Christian Brennecke (Universität Bonn)
11:30 - 12:30
Title and abstract: TBA
14:15
MCQM Seminar: Simone Warzel (Technische Universität München)
MCQM Seminar: Simone Warzel (Technische Universität München)
14:15 - 15:15
Title and abstract: TBA
Thursday, 30 May 2024
Friday, 31 May 2024