Itinerant Quantum Math Meetings

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)

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SPEAKER: Meriem Abdelaziz (University of Biskra)

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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)

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SPEAKER: Lorenzo Pettinari (University of Trento)

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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

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SPEAKER: Ian Jauslin (Rutgers University)

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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.

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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)

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).

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.