Category: Seminar PoliMi

Wednesday, November 27, 2024 - 9:00 - 12:30

Sala Consiglio (7th floor), D-Mat
Mathematics Department of PoliMi
Campus Leonardo, bd.14 "Nave".

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Program:

9:00 Karim Thebault (Bristol): “The Universe as an Open Quantum System”

9:45 Mike Cuffaro (Munich): “The Open Systems View (and Algebraic Quantum Field Theory)”

Coffee break

11:00 Sebastien Rivat (Munich): “The Open Systems View in Field Theory”

11:45 Michele Correggi (PoliMi): Quasi-classical Limit of a Spin Coupled to a Reservoir

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Description

The existence of open systems in physics poses outstanding philosophical issues. Indeed, while closed systems can be studied in isolation from the rest of the universe, open systems interact with the environment by exchanging heat and work, information, or matter. As such, open systems are subjected to changes due to uncontrollable external influences, which makes it challenging to precisely determine their properties. Since typical systems in the physical universe are not isolated, providing an adequate description of open systems lies at the heart of contemporary physics. In quantum theory, this issue is further complicated by the presence of entanglement between distant systems. Even more puzzling, at a cosmological scale, it is still a controversial matter whether the whole universe should be considered a closed or open system. The present workshop brings together philosophers and mathematical physicists to discuss the foundations of open systems both from a formal and a conceptual point of view. The invited speakers are Mike Cuffaro (Munich), Michele Correggi (PoliMi), Karim Thebault (Bristol) and Sebastien Rivat (Munich).

Organizing Committee: Antoine Brandelet, Massimo Moscolari and Giovanni Valente – Department of Mathematics, Politecnico di Milano

Participation is free of charge.

Funding: The conference is funded by Line 3 of the “Dipartimento di Eccellenza 2023-2027” on Mathematical features of quantum mechanics (Principal Investigator: Prof. Correggi), and by the Italian Ministry of University and Research within the PRIN 2022 project Analogical Reasoning in Contemporary Physical Theories (ID: 2022F4Z8YH, Principal Investigator: Giovanni Valente).

Wednesday, October 30, 2024 - 14:00

Sala Consiglio (7th floor), D-Mat
Mathematics Department of PoliMi
Campus Leonardo, bd.14 "Nave".

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Semi-classical measures, two scale semi-classical measures and applications

In this lecture, we will present semi-classical measures and show how they  describe the obstructions to strong convergence of bounded families of square integrable functions. We will also describe applications for families of solutions to PDEs, in particular to wave equations.

This initiative is part of the “PhD Lectures” activity of the project “Departments of Excellence 2023-2027” of the Department of Mathematics of    Politecnico di Milano. This activity consists of seminars open to PhD students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk.

Wednesday, October 9, 2024 - 15:00
Thursday, October 10, 2024 - 11:30

Sala Consiglio (7th floor), D-Mat
Mathematics Department of PoliMi
Campus Leonardo, bd.14 "Nave".

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A quantitative approach to entanglement theory via hypothesis testing (Oct. 9)

I will start by presenting the notion of entanglement as studied in quantum information theory. According to this definition, originally proposed by Werner in 1989, a density operator on a bipartite quantum system is declared to be entangled if it cannot be written as a convex combination of tensor products of single-system density operators, and separable (or unentangled) otherwise. I will then discuss the basics of quantum hypothesis testing and introduce the task of “entanglement testing”, which consists in discriminating a given entangled state from the set of all separable states. This task is a fundamental quantum information primitive, with applications ranging from device certification to gravitational entanglement detection. I will finish by discussing the statement of the “generalised quantum Stein’s lemma”, which connects the ultimate efficiency of entanglement testing with a key entanglement measure known as “relative entropy of entanglement”.

A solution of the generalised quantum Stein’s lemma (Oct. 10)

I will discuss the solution of the generalised quantum Stein’s lemma presented in [Lami, arXiv:2408.06410] (see also [Hayashi/Yamasaki, arXiv:2408.02722] forrelated work), which establishes that the Stein exponent associated with entanglement testing, namely, the quantum hypothesis testing task of distinguishing between n copies of an entangled state and a generic separable state, equals the regularised relative entropy of entanglement. To solve the problem I will briefly introduce two techniques. The first is a procedure called “blurring”, which, informally, transforms a permutationally symmetric state by making it more evenly spread across nearby type classes. I will discuss this technique extensively in the classical case, where it already suffices to prove the generalised Stein’s lemma. Depending on time, I will then present a second technical innovation, which is needed to prove the quantum version of the statement. This consists in a second quantisation step, which lifts the problem from a finite-dimensional system to an infinite-dimensionalbosonic quantum system, where it can then be solved with techniques from continuous-variable quantum information. Rather remarkably, the second-quantised action of the blurring map corresponds to a pure loss channel.


This initiative is part of the “PhD Lectures” activity of the project “Departments of Excellence 2023-2027” of the Department of Mathematics of Politecnico di Milano. This activity consists of seminars open to PhD students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk.

Thursday, May 30, 2024 and Friday, May 31, 2024 - 10:00
Sala Consiglio VII Piano, D-Mat
Politecnico di Milano
Ed. 14 "Nave", Campus Leonardo

SPEAKER: Andrea Posilicano (Università dell’Insubria)

Self-adjoint extensions by a Krein-type resolvent formula

We present a simple recipe to build all the self-adjoint extensions of a symmetric operator S which is the restriction of a given self-adjoint one. This provides the resolvent of the extensions and requires knowledge of neither the defect spaces nor the adjoint of S. Some applications to quantum mechanical models are given.

This initiative is part of the “PhD Lectures” activity of the project “Departments of Excellence 2023-2027” of the Department of Mathematics of Politecnico di Milano. This activity consists of seminars open to PhD students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk.

Monday, May 20, 2024 - 10:00 , Wednesday, May 22, 2024 - 11:00, Friday, May 24, 2024 - 10:00
Sala Consiglio VII Piano, D-Mat
Politecnico di Milano
Ed. 14 "Nave", Campus Leonardo

SPEAKER: Hynek Kovarik (Università di Brescia)

Trace formulas for one-dimensional Schrödinger operators

One-dimensional Schroedinger operators satisfy certain identity, called the trace formula, which relates the scattering and spectral data of the operator in question with integral means of the corresponding potential. In this mini-course we will give a sketch of the proof of this formula and discuss some of its applications.

This initiative is part of the “PhD Lectures” activity of the project “Departments of Excellence 2023-2027” of the Department of Mathematics of Politecnico di Milano. This activity consists of seminars open to PhD students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk.

Tuesday, May 7, 2024 - 10:15 , Wednesday, May 8, 2024 - 11:00
Aula Seminari III Piano, D-Mat
Politecnico di Milano
Ed. 14 "Nave", Campus Leonardo

SPEAKER: Horia Cornean (Aalborg Universitet)

On the Landauer-Büttiker formalism

In the first part we will introduce the setting and prove some fundamental scattering results related to the existence and completeness of wave operators arising in mesoscopic systems, and also prove the “classical” Landauer-Büttiker formula for non-interacting systems. The second part will be about providing sufficient conditions such that the time evolution of a mesoscopic tight-binding open system with a local Hartree-Fock non-linearity converges to a self-consistent non-equilibrium steady state, which is independent of the initial condition from the “small sample”. We will also show that the steady charge current intensities are given by Landauer-Büttiker-like formulas, and make the connection with the case of weakly self-interacting many-body systems. In order to get a better idea of what the lectures will cover, see https://arxiv.org/abs/2309.01564 .

This initiative is part of the “PhD Lectures” activity of the project “Departments of Excellence 2023-2027” of the Department of Mathematics of Politecnico di Milano. This activity consists of seminars open to PhD students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk.

Monday, April 15, 2024 - 14:15 , Tuesday, April 16, 2024 - 14:15 and Friday, April 19, 2024 - 10:30
Sala Consiglio, D-Mat
Politecnico di Milano
Ed. 14 "Nave", Campus Leonardo

SPEAKER: Jérémy Faupin & Sébastien Breteaux (Institut Élie Cartan de Lorraine – Université de Metz)

Number of bound states for fractional Schrödinger operators

Estimating the number of bound states (i.e. the number of negative eigenvalues counting multiplicities) of the two-body Schrödinger operator -Δ+V(x) on L²(ℝᵈ) constitutes a rich problem that has attracted lots of attention in the mathematical literature. This series of lectures will focus on bounds on the number of bound states for fractional Schrödinger operators (-Δ)ˢ+V(x) on L²(ℝᵈ), for any s>0 and in any spatial dimension d≥1. In the subcritical case s<d/2, we will in particular review the celebrated Cwikel-Lieb-Rozenblum bounds, while in the super-critical case s≥ d/2, we will report on a recent joint work with V. Grasselli.

This initiative is part of the “PhD Lectures” activity of the project “Departments of Excellence 2023-2027” of the Department of Mathematics of Politecnico di Milano. This activity consists of seminars open to PhD students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk.

Monday, March 4, 2024 - 14:15 and Thursday, March 7, 2024 - 10:15
Sala Consiglio
Dipartimento di Matematica
Politecnico di Milano
Ed. 14 "Nave", Campus Leonardo

SPEAKER: Stefan Teufel (Eberhard Karls Universität Tübingen)

Quantisation of Hall conductivity in infinite interacting fermion systems

Understanding the exact quantisation of the experimentally observed Hall
conductivity has led to many interesting developments also in mathematical
physics and to two Nobel prizes in physics. Although the problem is now more
than 40 years old, significant progress has been made on a rigorous level for
interacting systems in the last ten years. In my talk I will briefly review
some of the mathematical highlights of this development and then present a new result: We consider infinite systems of interacting electrons on a lattice
governed by a translation-invariant Hamiltonian with a unique gapped ground
state. Using the NEASS approach, we show that the Hall conductivity of such a
system at zero temperature is given by a many-body version of the famous
double-commutator formula without power-law corrections. We also show that this formula takes only quantised values. The main novelty compared to
existing mathematical results is that we consider the conductivity instead of
the conductance, and that working directly in infinite volume simplifies and
clarifies some arguments, provided one is willing to work in the C^*-algebraic
framework used in the mathematical description of such systems.

In the first lecture I will mainly talk about the history of the problem and set up the mathematical framework. In the second lecture I will present the new results. The latter are based on joint work with Giovanna Marcelli, Tadahiro Miyao, Domenico Monaco and Marius Wesle.

This initiative is part of the “PhD Lectures” activity of the project “Departments of Excellence 2023-2027” of the Department of Mathematics of Politecnico di Milano. This activity consists of seminars open to PhD students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk.

Tuesday, February 6, 2024 – 14:15
Sala Consiglio
Dipartimento di Matematica
Politecnico di Milano
Ed. 14 “Nave”, Campus Leonardo

SPEAKER: Marco Olivieri (University of Copenhagen)

A novel method for the derivation of the free energy expansion of the Bose gases

We present an innovative method to derive the expansion of the free energy
density of a dilute Bose gas in thermodynamic regime in dimension three. In the first part of the talk, we give a gentle introduction on the thermodynamic limit as the optimal tool for the macroscopic derivation of the thermodynamics from the quantum statistical mechanics. In the second part of the talk, we will focus our attention on the macroscopic behavior of Bose gases, which have a phase transition to Bose Einstein condensates for low temperature. We then study a gas of many bosons interacting through a spherical, pairwise, positive potential. Using a combination of the renormalization of the potential, the Neumann localization and Bogoliubov diagonalization, we derive a lower bound for the second order expansion of the free energy.

This initiative is part of the “PhD Lectures” activity of the project “Departments of Excellence 2023-2027” of the Department of Mathematics of Politecnico di Milano. This activity consists of seminars open to PhD students, followed by meetings with the speaker to discuss and go into detail on thetopics presented at the talk.

Monday, Jan 15, 2024 – 15:00 Aula Seminari III piano (III fl)
Wednesday, Jan 17, 2024 – 15:00 Sala Consiglio (VII fl)
Mathematics Department, Politecnico di Milano
Ed. 14 (Nave), Campus Leonardo, Milano, Italy

SPEAKER: Alessandro Giuliani (Università degli Studi di Roma Tre)

Universality of the critical conductivity of the Haldane-Hubbard model

The Haldane model is a standard tight binding model describing electrons hopping on a hexagonal lattice subject to a transverse, dipolar, magnetic field. We consider its interacting version and study the critical case at the transition between the trivial and the “topological” insulating phases. In previous works,
we proved the quantization of the critical longitudinal conductivity for weak enough interaction strength. We now report a recent extension of the result to the critical transverse conductivity, which turns out to be quantized at half-integer values, irrespective of the interaction strength. Proofs are based on a combination of constructive Renormalization Group methods and exact lattice Ward Identities. Joint works with S. Fabbri, V. Mastropietro, M. Porta, R. Reuvers.

The talk will be divided in two parts: in part 1, motivations, main results and main ideas of the proof will be stated and explained. Part 2 will be more technical and will discuss in more detail some selected aspects of the proof.

This initiative is part of the “PhD Lectures” activity of the project “Departments of Excellence 2023-2027” of the Department of Mathematics of Politecnico di Milano. This activity consists of seminars open to PhD students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk.