Month: April 2025

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.

________________________________________________________________________

SPEAKER: Douglas Lundholm (Uppsala Universitet)

________________________________________________________________________

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.

________________________________________________________________

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)

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.

________________________________________________________________________

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).