Category: Seminar UniMi

Wednesday, April 15, 2026 - 16:15
Aula M02 - Via Mangiagalli, 31
Università degli Studi di Milano

Zoom link on request (contact Niels Benedikter by email)

_______________________________________________________________

SPEAKER: Meriem Abdelaziz (University of Biskra)

________________________________________________________________

Analytical Solutions of the Schrödinger Equation for Diatomic Molecules in Deformed Spaces

In this work, we investigate the analytical solutions of the Schrödinger equation for diatomic molecular systems using the pseudo-harmonic and Kratzer potentials. The study is carried out in both standard quantum mechanics and in deformed frameworks, namely de Sitter and anti-de Sitter spaces, incorporating the effects of the Extended Uncertainty Principle (EUP). By applying the extended Nikiforov–Uvarov method, we derive explicit expressions for the energy eigenvalues and corresponding wave functions. The influence of quantum deformation on the spectral properties of selected diatomic molecules is analyzed, highlighting potential implications for quantum technologies.

Wednesday, March 18, 2026 - 11:30
Aula 305 - Via Golgi 18/20 (Settore didattico)
Università degli Studi di Milano

Zoom link on request (contact Niels Benedikter by email)

_______________________________________________________________

SPEAKER: Lorenzo Pettinari (University of Trento)

________________________________________________________________

Damping of phonons in Bose gas at low temperature

Condensed Bose gases can be effectively described in terms of quasi-particles, commonly referred to as phonons. Their dynamics are captured by a c-number ondensate Hamiltonian consisting of a quadratic term supplemented by third- and fourth-order perturbative corrections. These additional interaction terms render the phonons unstable, giving rise to two distinct decay processes known as Beliaev and Landau damping. From a mathematical perspective, such decay mechanisms should manifest as a broadening of the Bogoliubov dispersion relation in the thermodynamic limit. To validate this picture, I will present two different approaches to deriving the phonon decay rates. The first is inspired by the W*-algebraic framework of Jaksic-Pillet, employing Standard Representations and perturbative expansions of a suitably chosen vector state. The second method is based on the analysis of two-body correlation functions. Both approaches yield the same imaginary correction to the Bogoliubov dispersion relation, which in turn determines the expected broadening. urthermore, our approaches offer a new perspective on the decay of phonons in terms of the left and right components of these quasi-particles. The talk is based on joint work with Jan Derezi´nski and may be viewed as a modern laboration of the classical contributions of Beliaev, Hohenberg–Martin, and others.

Monday, January 12, 2026 - 14:00
Aula C01 - Via Luigi Mangiagalli, 25
Università degli Studi di Milano

_______________________________________________________________

SPEAKER: Ian Jauslin (Rutgers University)

________________________________________________________________

A framework to study twisted bilayer graphene in a tight binding model

The study of the electronic properties of twisted bilayer graphene (TBG) has garnered much attention from the condensed matter community recently. TBG is obtained by stacking two graphene monolayers on top of each other, and rotating one of them with respect to the other. Theoretical and experimental analyses have found that the electronic properties of TBG depend very strongly on the angle between the layers. In fact, a handful of “magic” angles have been predicted at which TBG becomes a supercondutor, and this has even been verified experimentally.

The model commonly used to study TBG is an effective one, and was derived by
Bistritzer and MacDonald. In this talk, I will present recent results on developing a framework to study TBG from first principles. To be more exact, we consider a tight-binding model for the electrons, but make no further approximations. Using a renormalization group technique, we construct a perturbative expansion to study TBG that is convergent when the twisting angle satisfies certain diophantine conditions.

This is joint work with V. Mastropietro.

Friday, April 11, 2025

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

________________________________________________________________

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

________________________________________________________________

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)

Thursday, April 3, 2025 - 11:00

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

________________________________________________________________________

SPEAKER: Antoine Borie (Université de Rennes)

________________________________________________________________________

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).

Wednesday, December 6, 2024 - 14:00

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

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.

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

________________________________________________________________________

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.

Tuesday, May 7, 2024 - 11:30
Sala di rappresentanza
Dipartimento di Matematica
Università degli Studi di Milano
Via Cesare Saldini 50

---

SPEAKER: Cornelia Vogel (Universität Tübingen)

---

Concentration of measure for thermal distributions of quantum states

We generalize Lévy’s Lemma, a concentration-of-measure result for the uniform probability distribution on high-dimensional spheres, to a more general class of measures, so-called GAP measures. For any given density matrix ρ on a separable Hilbert space H, GAP(ρ) is the most spread out probability measure on the unit sphere of H that has density matrix ρ and thus forms the natural generalization of the uniform distribution. We prove concentration-of-measure whenever the largest eigenvalue ||ρ|| of ρ is small. With the help of this result we generalize the well-known and important phenomenon of ”canonical typicality” to GAP measures. Canonical typicality is the statement that for ”most” pure states ψ of a given ensemble, the reduced density matrix of a sufficiently small subsystem is very close to a ψ-independent matrix. So far, canonical typicality is known for the uniform distribution on finite-dimensional spheres, corresponding to the micro-canonical ensemble. Our result shows that canonical typicality holds in general for systems described by a density matrix with small eigenvalues. Since certain GAP measures are quantum analogs of the canonical ensemble of classical mechanics, our results can also be regarded as a version of equivalence of ensembles. The talk is based on joint work with Stefan Teufel and Roderich Tumulka.

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

_________________________________________________________________________

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.

Monday, March 18, 2024 - 11:15
Aula Dottorato (first floor)
Dipartimento di Matematica
Università degli Studi di Milano
Via Cesare Saldini 50

---

SPEAKER: Zhituo Wang (Harbin Institute of Technology)

---

Constructive renormalizations of the 2-D Honeycomb-Hubbard model

In this talk I will present some recent progress on the construction of ground state of the 2-dimensional Hubbard model, which is a prototypical model for studying phase transitions in quantum many-body system. Using fermionic cluster expansions and constructive renormalization theory, we proved that the ground state of the 2-d Hubbard model on the honeycomb lattice with triangular Fermi surfaces is not a Fermi liquid in the mathematical precise sense of Salmhofer. I will also discuss the crossover phenomenon in the 2-d square Hubbard model and universalities. This presentation is based on the work arXiv:2108.10852, CMP 401, 2569–2642(2023) and arXiv:2303.13628.