Author: Ngọc Nhi Nguyễn

28-29-30/04/2025 & 5-6/05/2025 : Douglas Lundholm @PoliMi

Ngọc Nhi NguyễnSeminar PoliMi 
Schedule:   Monday, April 28th, 14.00 - 16.00
            Tuesday, April 29th, 10:00 - 12:00
            Wednesday, April 30, 14:00 - 16:00
            Monday, May 5th, 14:00 - 16:00
            Wednesday, May 7th, 14:00 - 16:00


Aula Seminari (3rd floor)
Bd. 14 "Nave", Via Bonardi 9,
D-Mat Mathematics Department of PoliMi, Politecnico di Milano.

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SPEAKER: Douglas Lundholm (Uppsala Universitet)

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Mathematics of the 2D anyon gas

In the theory of quantum statistics, if one follows mathematical logic to its conclusion, one reaches the possibility of intermediate exchange statistics and “anyons”, i.e. identical particles different from bosons and fermions. Over the course of about 50 years this topic has evolved from merely an exotic possibility to an almost inevitability when orientation symmetry is broken, such as in effectively two-dimensional systems subject to rotation or an external magnetic field. The signature example is the fractional quantum Hall effect, and in just the last few years very strong signatures of individual anyons have finally arrived from experiments. However, the many-body theory necessary to study precise collective properties of anyons has remained rather undeveloped until relatively recently. This mini course will focus on the mathematics of the many-anyon gas, introduce some of the main concepts involved, and thus provide a foundation for further exploration of the topic, starting from the toy model of ideal anyons, to more realistic emergent models, and also promising applications to quantum computing.

Lecture plan:

I. Quantum statistics & transmutation

II. Local exclusion & stability

III. The almost-bosonic interacting anyon gas

IV. Emergent models: FQHE & polarons

V. Non-abelian anyons & topological quantum computing

Further information: https://sites.google.com/view/qmp25-intensiveperiod/courses

11/04/2025 : Annalisa Panati @UniMi

Ngọc Nhi NguyễnSeminar UniMi 
Friday, April 11, 2025

Aula 6,
Dipartimento di Matematica,
Università degli Studi di Milano,
Via Cesare Saldini 50.

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SPEAKER: Annalisa Panati (Université de Toulon, Centre de Physique Théorique)

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Entropic fluctuations in quantum two-time measurement framework

Non-equilibrium statistical mechanics has seen some impressive developments in the last three decades, since the ground-breaking formulation of the transient and steady entropic Fluctuation Relations (FR) in the early nineties.
The extension of these results to the quantum setting has turned out to be surprisingly challenging and it is still an ongoing effort. Kurchan and Hal Tasaki’s seminal works (2000) showed quantum formulation of the transient version of FR is possible by introducing the two-time measurement framework.
In this talk, we present some results in a recent series of papers, where we attempt to introduce a quantum equivalent of steady entropic functional and compare it to the transient version for open quantum system. We consider both the case of idealised direct measurement on the reservoirs and experimentally accessible indirect measurement through coupling with an ancilla. We analyse in particular stability with respect to the initial state. In order to deal with the thermodynamic limit and to have general results, we use methods of $C^*$- algebras and modular theory.


(Joint work with T. Benoist, L. Bruneau, V. Jakšić, C.A. Pillet)

03/04/2025 : Antoine Borie @UniMi

Ngọc Nhi NguyễnSeminar UniMi 
Thursday, April 3, 2025 - 11:00

Aula dottorato,
Dipartimento di Matematica,
Università degli Studi di Milano,
Via Cesare Saldini 50.

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SPEAKER: Antoine Borie (Université de Rennes)

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Scattering for the positive density Hartree equation

In this talk, we explore the long-time behavior of solutions to of the positive density Hartree equation, which models the evolution of a homogeneous quantum gas. Our focus is the stability of certain stationary states, extending the original result introduced by Mathieu Lewin and Julien Sabin to higher dimensions and more singular interaction potentials. Using tools from dispersive partial differential equations, such as Strichartz estimates and fractional Leibniz rules, we develop a new approach tailored to density matrices.

This talk is based on joint work with Julien Sabin (Rennes University ) and Sonae Hadama (Kyoto University).

17/12/2024 : Jonas Lampart @PoliMi

Ngọc Nhi NguyễnSeminar PoliMi 
Tuesday, December 17, 2024 - 11:30

Aula Seminari MOX (6th floor), D-Mat
Mathematics Department of PoliMi
Campus Leonardo, bd.14 "Nave".

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SPEAKER: Jonas Lampart (CNRS & Université de Bourgogne)

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Superfluidity and the spectrum of polaron Hamiltonians

I will discuss how superfluidity manifests itself in the spectrum of the Hamiltonian for a test particle travelling through a Bose Einstein condensate.

In the Bogoliubov-Fröhlich polaron model, a stable polaron with momentum P corresponds to a ground state of the Hamiltonian at fixed total momentum. I will explain a recent result in collaboration with Benjamin Hinrichs, which shows that a ground state exists if the momentum is less than mc, where m is the particle mass and c is the slope at zero momentum of the dispersion relation of the Bogoliubov phonons.

06/12/2024 Pierre Roux @UniMi

Ngọc Nhi NguyễnSeminar UniMi 
Wednesday, December 6, 2024 - 14:00

Aula Dottorato,
Dipartimento di Matematica,
Università degli Studi di Milano,
Via Cesare Saldini 50.

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SPEAKER: Pierre Roux (Institut Camille Jordan, École Centrale de Lyon)

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Disentangling pulse-coupled oscillators in the mean-field regime through the pseudo-inverse in a dilated timescale

Systems of pulse-coupled oscillators model synchronization through singular interactions occurring at discrete times, when particles reach a specific firing phase. They have numerous applications in physics, biology and engineering, for example to cardiac cells, neurons and fireflies. In the mean-field limit, the probability density in phase satisfies a singular continuity equation prone to finite-time blow-up, for which very few theoretical results are available. With José A. Carrillo, Xu’an Dou and Zhennan Zhou, we have introduced a reformulation of the mean-field system based on the inverse distribution function seen in a dilated timescale. It allows to show a hidden contraction/expansion mechanism and to propose simple and rigorous proofs of the long-time behaviour, the existence of steady states, the rates of convergence and the occurence of finite time blow-up for a large class of monotone phase response functions.

30/10/2024 : Clotilde Fermanian Kammerer @PoliMi

Ngọc Nhi NguyễnSeminar PoliMi 
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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SPEAKER: Clotilde Fermanian Kammerer (Université d’Angers)

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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.

9 &10/10/2024 : Ludovico Lami @PoliMi

Ngọc Nhi NguyễnSeminar PoliMi 
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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SPEAKER: Ludovico Lami (University of Amsterdam)

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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.

05/06/2024 : Umberto Morellini @UniMi

Ngọc Nhi NguyễnSeminar UniMi 
Wednesday, June 5, 2024 - 11:15
Sala di Rappresentanza
Dipartimento di Matematica
Università degli Studi di Milano
Via Cesare Saldini 50

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SPEAKER: Umberto Morellini (Université Paris Dauphine, CEREMADE, PSL) ________________________________________________________________________

The free energy of Dirac’s vacuum in purely magnetic fields

The Dirac vacuum is a non-linear polarisable medium rather than an empty space. This non-linear behaviour starts to be significant for extremely large electromagnetic fields such as the magnetic field on the surface of certain neutron stars. Even though the null temperature case was deeply studied in the past decades, the problem at non-zero temperature needs to be better understood.
In this talk, we will present the first rigorous derivation of the one-loop effective magnetic Lagrangian at positive temperature, a non-linear functional describing the free energy of quantum vacuum in a classical magnetic field. After introducing our model, we will properly define the free energy functional using the Pauli-Villars regularisation technique in order to remove the worst ultraviolet divergences, which represent a well known issue of the theory. The study of the properties of this functional will be addressed before focusing on the limit of slowly varying classical magnetic fields. In this regime, one can prove the convergence of this functional to the Euler-Heisenberg
formula with thermal corrections, recovering the effective Lagrangian first derived by Dittrich in 1979. The talk is based on the work available at arXiv:2404.12733.

22/04/2024: Antoine Prouff @UniMi

Ngọc Nhi NguyễnSeminar UniMi 
Monday, April 22, 2024 - 11:15
Sala di Rappresentanza
Dipartimento di Matematica
Università degli Studi di Milano
Via Cesare Saldini 50

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SPEAKER: Antoine Prouff (Université Paris-Saclay, Laboratoire de Mathématique d’Orsay) _________________________________________________________________________

Egorov’s theorem in the Weyl-Hörmander calculus and application to the control of PDEs

It is known that geometric optics can be derived as the high-frequency limit of the wave equation, from both experimental and theoretical perspectives. This fact can be regarded as an instance of a “quantum-classical correspondence principle”, made rigorous by Egorov’s theorem, which relates the evolution of a linear PDE (e.g. the wave equation) to the natural underlying classical dynamics (e.g. the geodesic flow).

We will present a version of Egorov’s theorem in the Euclidean space, in the setting of the “Weyl-Hörmander calculus”. This general framework of microlocal analysis involves Riemannian metrics on the phase space adapted to the dynamics under consideration, and allows for a fairly large range of applications (study of Schrödinger, wave and transport equations).

If time allows, we will discuss in more detail an application to the observability of the Schrödinger equation with a confining potential in the Euclidean space.