04/03/2024: Joachim Kerner @ UniMi

Monday, March 4, 2024 - 11:15
Sala di Rappresentanza
Dipartimento di Matematica
Università degli Studi di Milano
Via Cesare Saldini 50

SPEAKER: Joachim Kerner (FernUniversität in Hagen)


On Bose-Einstein Condensation in the Random Kac-Luttinger Model

This talk is concerned with a random many-particle model originally considered by Kac and Luttinger in 1973 in order to study a well-known quantum phase transition known as Bose–Einstein condensation (BEC). Generally speaking, to understand this phase transition in interacting many-particle systems is a current hot topic in mathematical physics. However, due to the complexity of the underlying random one-particle model, the nature of the BEC in the non-interacting Kac-Luttinger model was understood only recently based on results obtained by Alain-Sol Sznitman (ETH). In this talk, our goal will be to understand the impact of repulsive two-particle interactions on this condensate. We will see that, due to the spatial localization of the condensate, strong enough interactions will immediately destroy it. On the other hand, for two-particle interactions of a mean-field type, we prove BEC in the interacting Kac–Luttinger model into a minimizer of a Hartree-type functional. This talk is based on joint work with C. Boccato (Milan), M. Pechmann (Tennessee), and W. Spitzer (Hagen).

The seminar is part of the activities of the project PRIN 2022AKRC5P “Interacting Quantum Systems: Topological Phenomena and Effective Theories” financed by the European Union – Next Generation EU.

25/01/2024: Amirali Hannani @ UniMi

Thursday, January 25, 2024 - 11:15
Sala di Rappresentanza
Dipartimento di Matematica
Università degli Studi di Milano
Via Cesare Saldini 50

SPEAKER: Amirali Hannani (KU Leuven)


Localization and Poisson statistics in the “avalanche model”

The “avalanche model” aka “quantum sun model” has been introduced as a toy model to study the stability of the MBL (Many-body localized) phase. Strong numerical and theoretical heuristics suggest a localization-delocalization transition in this family of models varying a natural parameter $\alpha$. We prove localization (in the many-body sense) and Poisson statistics for this model given $\alpha$ sufficiently small. In this talk, first I give some general preliminaries about MBL (Many-body localization) which motivate the above-mentioned model. Then I introduce the model and recall certain numerical “facts” about the localized phase. Finally, I state our theorem concerning localization and Poisson statistics and give some ideas about the proof which rests on showing certain weak information about the absence of level-attractions in this model. This is a joint work with Wojciech De Roeck (KU Leuven).

26/02/2024: Emanuela Giacomelli @ UniMi

Monday, February 26, 2024 - 11:15
Sala di Rappresentanza
Dipartimento di Matematica
Università degli Studi di Milano
Via Cesare Saldini 50

SPEAKER: Emanuela Giacomelli (LMU München)


The low density Fermi gas in three dimensions

In recent decades, the study of many-body systems has been an active area of research in both physics and mathematics. In this talk we consider a system of N interacting fermions with spin 1/2 confined in a box in the dilute regime. We are interested in studying the correlation energy, defined as the difference between the energy of the fundamental state and that of the free Fermi gas. We will discuss some recent results on a first-order asymptotic for the correlation energy in the thermodynamic limit, where the number of particles and the size of the box are sent to infinity while keeping the density fixed. In particular, we will present some recent results for the correlation energy that go in the direction of a rigorous proof of the well-known Huang-Yang formula of 1957.

15/01/2024: Clara Torres Latorre @ UniMi

Monday, January 15, 2024 - 11:15
Aula 9
Dipartimento di Matematica
Università degli Studi di Milano
Via Cesare Saldini 50

SPEAKER: Clara Torres Latorre (Universitat de Barcelona)


Regularity theory for elliptic and parabolic PDE

In this talk, we’ll explore how regularity theory is crucial for understanding partial differential equations (PDEs), and how it has consequences in physics and numerical analysis. We’ll first focus on why regularity matters, then take elliptic and parabolic PDEs as examples to talk about classical and recent regularity results. The goal is to give a practical overview, explaining when PDE solutions are smooth or singular.

13/07/2023: Diwakar Naidu @ UniMi

Thursday, July 13, 2023 - 15:00
Sala di Rappresentanza
Mathematics Department, University of Milan
Via Cesare Saldini 50, Milano, Italy

SPEAKER: Diwakar Naidu (Universität Tübingen)


Existence of Bell-type pure jump process for the Klein-Gordon Hamiltonian

In this talk I will present my work on Bell-type jump processes. J.S. Bell in
1984 gave a jump rate formula that predict the probability of configurational
jumps and in turn define a stochastic (Markov) jump process that governs the
evolution of particle configurations. The standard method (by Tumulka et al)
for proving existence of such processes does not work for the Klein-Gordon (KG) Hamiltonian as the jump rates for it are unbounded. We show the existence
of a stationary and independent (Markov) pure jump process (i.e. where the
configurational motion occurs only via jumps) for the particle configuration that
is equivariant, i.e. |Ψt|2 distributed at every time t, where Ψ evolves with the KG
Hamiltonian, using elements from the theory of Lévy processes. Next, we also
want to extend this obtained process to a broader class of Markov process which also depend on the particle configurations and time using the general theory of Markov processes.

9/10/2023: Asbjørn Bækgaard Lauritsen @ UniMi

October 9, 2023 - 11:15
Sala di Rappresentanza
Mathematics Department, University of Milan
Via Cesare Saldini 50, Milano, Italy

SPEAKER: Asbjørn Bækgaard Lauritsen (IST Austria)


Ground state energy and pressure of a dilute spin-polarized Fermi gas

Recently the study of dilute quantum gases have received much interest, in particular regarding their ground state energies and pressures/free energies at positive temperature. I will present recent work on such problems. Namely that of the ground state energy of a spin-polarized Fermi gas and the extension to the pressure at positive temperature. Compared to the free gas, the energy density/pressure of the interacting gas differs by a term of order a^3 \rho^{8/3} with a the p-wave scattering length of the interaction. One of the main ingredients in the proofs is a rigorous version of a formal cluster expansion of Gaudin, Gillespie and Ripka (Nucl. Phys. A, 176.2 (1971), pp. 237-260). I will discuss this expansion and the analysis of its absolute convergence.

Joint work with Robert Seiringer.

5/6/2023: Andreas Deuchert @ UniMi

June 5, 2023 - 11:15
Aula dottorato, first floor
Università degli Studi di Milano
Via Saldini 50

SPEAKER: Andreas Deuchert (Universität Zürich)


Microscopic Derivation of Ginzburg-Landau Theory and the BCS Critical Temperature Shift in General External Fields

We consider the Bardeen-Cooper-Schrieffer (BCS) free energy functional with weak and macroscopic external electric and magnetic fields and derive the Ginzburg-Landau functional. We also provide an asymptotic formula for the BCS critical temperature as a function of the external fields. This extends our previous results in arXiv:2105.05623 for the constant magnetic field to general magnetic fields with a nonzero magnetic flux through the unit cell. This is joint work with C. Hainzl and M. Maier.

11/07/2023: Davide Lonigro @ UniMi

July 11, 2023 - 15:00
Sala di Rappresentanza (ground floor on the left)
Mathematics Department, University of Milan
Via Cesare Saldini 50, Milano, Italy

SPEAKER: Davide Lonigro (Università degli Studi di Bari)


Self-adjointness of a class of spinboson models with ultraviolet divergences 

We study a class of quantum Hamiltonian operators describing a family of two-level systems (spins) coupled with a structured boson field, with a rotating-wave coupling mediated by form factors possibly exhibiting ultraviolet divergences (hence, non-normalizable). Spin–spin interactions which do not modify the total number of excitations are also included. Starting from the single-atom case, and eventually reaching the general scenario, we shall provide explicit expressions for the self-adjointness domain and the resolvent operator of such models. This construction is also shown to be stable, in the norm resolvent sense, under approximations of the form factors by normalizable ones, for example an ultraviolet cutoff.

13/02/2023 – 15/03/2023: Matteo Gallone @ UniMi

13/02  14:00-16:00   Sala di rappresentanza, ground floor, Mathematics Department, Via C. Saldini 50
14/02  10:00-12:00   Aula dottorato, first floor, Mathematics Department, Via C. Saldini 50
15/02  10:00-12:00   Aula dottorato, first floor, Mathematics Department, Via C. Saldini 50
1/03   14:00-16:00   Aula Mp, Via Mangiagalli 32
2/03   10:00-12:00   Aula dottorato, first floor, Mathematics Department, Via C. Saldini 50
3/03   10:00-12:00   Aula dottorato, first floor, Mathematics Department, Via C. Saldini 50
13/03  14:00-16:00   Aula C10, Via Mangiagalli 25
14/03  10:00-12:00   Aula dottorato, first floor, Mathematics Department, Via C. Saldini 50
15/03  10:00-12:00   Aula dottorato, first floor, Mathematics Department, Via C. Saldini 50

SPEAKER: Matteo Gallone (SISSA Trieste)


Introduction to Renormalisation Group for Fermionic Models

This series of seminars presents techniques used to rigorously approach the analysis of statistical mechanical systems of fermions. These include:
i) Gaussian integration using Feynman graphs
ii) Grassmann variables and Grassmann Gaussian integration
iii) ​Grassmann representation of the 2D Ising Model with quasi-periodic disorder
iv) Decay of the 2-point correlation function.

Students may get credit (in the category of seminar type F) for this course. Please contact Niels Benedikter if you intend to receive credit: niels.benedikter__A_T__unimi.it

24/11/2022: Luca Fresta @ UniMi

November 24, 2022, 15:45
Sala di Rappresentanza
Mathematics Department, University of Milan
Via Cesare Saldini 50, Milano, Italy

SPEAKER: Luca Fresta (Universität Bonn)


Stochastic Analysis of Subcritical Euclidean Fermionic Field Theories

In my talk, I will introduce a forward-backward stochastic differential equation
which provides a stochastic quantisation of subcritical Grassmann measures. The method is inspired by the so-called continuous renormalisation group, but
avoids the technical difficulties encountered in the direct study of the Polchinski’s flow equation for the effective potentials. If time permits, I will also show how to prove the exponential decay of correlations by a coupling method.
Work in collaboration with De Vecchi and Gubinelli.