04/03/2024: Joachim Kerner @ UniMi

quantumseminarSeminar 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.

06/02/2024: Marco Olivieri @ PoliMi

Marco FalconiSeminar PoliMi

Tuesday, February 6, 2024 – 14:15
Sala Consiglio
Dipartimento di Matematica
Politecnico di Milano
Ed. 14 “Nave”, Campus Leonardo

SPEAKER: Marco Olivieri (University of Copenhagen)

A novel method for the derivation of the free energy expansion of the Bose gases

We present an innovative method to derive the expansion of the free energy
density of a dilute Bose gas in thermodynamic regime in dimension three. In the first part of the talk, we give a gentle introduction on the thermodynamic limit as the optimal tool for the macroscopic derivation of the thermodynamics from the quantum statistical mechanics. In the second part of the talk, we will focus our attention on the macroscopic behavior of Bose gases, which have a phase transition to Bose Einstein condensates for low temperature. We then study a gas of many bosons interacting through a spherical, pairwise, positive potential. Using a combination of the renormalization of the potential, the Neumann localization and Bogoliubov diagonalization, we derive a lower bound for the second order expansion of the free energy.

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 thetopics presented at the talk.

Lecture Series: Alessandro Giuliani @ PoliMi

Marco FalconiSeminar PoliMi

Monday, Jan 15, 2024 – 15:00 Aula Seminari III piano (III fl)
Wednesday, Jan 17, 2024 – 15:00 Sala Consiglio (VII fl)
Mathematics Department, Politecnico di Milano
Ed. 14 (Nave), Campus Leonardo, Milano, Italy

SPEAKER: Alessandro Giuliani (Università degli Studi di Roma Tre)

Universality of the critical conductivity of the Haldane-Hubbard model

The Haldane model is a standard tight binding model describing electrons hopping on a hexagonal lattice subject to a transverse, dipolar, magnetic field. We consider its interacting version and study the critical case at the transition between the trivial and the “topological” insulating phases. In previous works,
we proved the quantization of the critical longitudinal conductivity for weak enough interaction strength. We now report a recent extension of the result to the critical transverse conductivity, which turns out to be quantized at half-integer values, irrespective of the interaction strength. Proofs are based on a combination of constructive Renormalization Group methods and exact lattice Ward Identities. Joint works with S. Fabbri, V. Mastropietro, M. Porta, R. Reuvers.

The talk will be divided in two parts: in part 1, motivations, main results and main ideas of the proof will be stated and explained. Part 2 will be more technical and will discuss in more detail some selected aspects of the proof.

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.

25/01/2024: Amirali Hannani @ UniMi

Sascha LillSeminar 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

quantumseminarSeminar 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

quantumseminarSeminar 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.

Lecture Series: Nicola Pinamonti @ PoliMi

Marco FalconiSeminar PoliMi 
Monday, Nov 20, 2023 - 15:15 Sala Consiglio (VII fl)
Tuesday, Nov 21, 2023 - 11:15 Sala Consiglio (VII fl)
Thursday, Nov 23, 2023 - 14:15 Sala Seminari MOX (VI fl)
Mathematics Department, Politecnico di Milano
Ed. 14 (Nave), Campus Leonardo, Milano, Italy

SPEAKER: Nicola Pinamonti (University of Genova)

Aspects of free and interacting quantum field theories on curved backgrounds

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.

30/10/2023: Alain Joye @ PoliMi

Marco FalconiSeminar PoliMi 
Monday, October 30, 2023 - 16:15
Sala Consiglio
Mathematics Department, Politecnico di Milano
VII Floor, Ed. 14 (Nave), Campus Leonardo, Milano, Italy

SPEAKER: Alain Joye (Université Grenoble Alpes)

Quantum Walks: Deterministic and Random

The concept of quantum walks on a graph has gained popularity in the scientific literature in recent years, likely due to its intersection between theoretical computer science, physics, and mathematics. After providing an overview of some popular quantum walks to illustrate their significance in these fields, we will focus on the quantum walks commonly referred to as “coined quantum walks” in the literature. Taking a discrete dynamical system perspective on these quantum walks, we will then discuss some of their transport properties in various regimes, both random and deterministic. This discussion will highlight the differences and similarities between coined quantum walks and classical random walks.

This initiative is part of the “PhD Lectures” activity of the project
“Departments of Excellence 2023-2027”, consisting of seminars open to
Ph.D. students, followed by meetings with the speaker to discuss and go into
detail on the topics presented at the talk.

13/07/2023: Diwakar Naidu @ UniMi

quantumseminarSeminar 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.

12/07/2023: Giuseppe De Nittis @ PoliMi

Marco FalconiSeminar PoliMi 
July 12, 2023 - 15:00
Aula Seminari III piano, third floor
Politecnico di Milano
Campus Leonardo, Ed. 14 (Nave)

SPEAKER: Giuseppe De Nittis (Pontificia Universidad Católica de Chile)

About the notion of eigenstates in C*-algebras and some application to quantum mechanics

This talk is concerned with the notion of eigenstates of an operator in an abstract C*-algebra. After reviewing some basic and structural results, I will explore the possibility of reinterpreting certain typical concepts of quantum mechanics (dynamical equilibrium states, ground states, gapped states, Fermi surfaces) in terms of (algebraic) eigenstates.

This is also part of the “PhD Lectures” activity of the project “Departments of Excellence 2023-2027”. This activity consists of seminars open to Ph.D. students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk.