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.

12/07/2023: Massimo Moscolari @ PoliMi

Marco FalconiSeminar PoliMi 
July 12, 2023 - 11:00
Aula Seminari III piano, third floor
Politecnico di Milano
Campus Leonardo, Ed. 14 (Nave)

SPEAKER: Massimo Moscolari (Politecnico di Milano)

On the bulk-edge correspondence for (interacting) fermion systems

I will first show that for general 2d random ergodic magnetic Schrödinger operators the bulk magnetization equals the total edge current at any temperature. The equality between the bulk and edge quantum transport indices can be then obtained as a corollary of our purely analytical argument by imposing a gap condition and by taking a “zero temperature” limit. After that, I will briefly show how to extend the equality of bulk magnetization and total edge current to lattice fermion systems with short-range interactions and above a certain critical temperature. The talk is based on joint works with Horia Cornean, Jonas Lampart, Stefan Teufel and Tom Wessel.

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.

9/10/2023: Asbjørn Bækgaard Lauritsen @ UniMi

quantumseminarSeminar 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.

IQMM talk LauritsenDownload

17/07/2023: Angelo Lucia @ PoliMi

Marco FalconiSeminar PoliMi 
July 17, 2023 - 16:00
Sala Consiglio, seventh floor
Politecnico di Milano
Campus Leonardo, Ed. 14 (Nave)

SPEAKER: Angelo Lucia (Universidad Complutense de Madrid)

Thermalization of quantum memories

Quantum memories are quantum spins systems designed to protect a quantum state from external noise. Contrary to the classical case, there are reasons to conjecture that there are no two-dimensional quantum memories that survive for long period of times at non-zero temperature.

In this talk, I will discuss a way to rigorously prove this conjecture, by estimating the mixing time of a class of
Quantum Markovian Semigroups. I will then present some recent results, regarding the case of so-called Kitaev’s quantum double models, for which we can perform such estimate and confirm the conjecture.

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.

6/7/2023: Domenico Finco @ UnIns

Claudio CacciapuotiSeminar UnIns 
July 6, 2023 - 16:15
Aula VA2, floor -1
Università degli Studi dell'Insubria
Via Valleggio 11, Como

SPEAKER: Domenico Finco (Università Telematica Uninettuno, Roma)

NLS with a Nonlinearity Concentrated on a Sphere

We discuss some existence results for the solutions of the NLS with nonlinearity concentrated on a sphere in dimension three.