Seminars and courses

Upon invitation of the scientific board, a number of international visiting scientists will be running seminars and mini-courses at the University of Bari, strengthening and complementing local research lines, and enhancing the interaction with local faculty and participants in the programme. 


Gianluca Orlando (Polytechnic University of Bari)

Title: Chirality transitions in a frustrated spin model

Abstract: Spin models are lattice models that describe magnetic properties of materials. In this talk we will examine a 2-dimensional planar spin model (known as the J1-J2-J3 model) which exhibits frustration. Frustration is the phenomenon due to conflicting interatomic ferromagnetic/antiferromagnetic interactions that prevent the energy of every pair of interacting spins to be simultaneously minimized. The frustration mechanism leads to complex geometric patterns in the material. We study these complex geometric patterns by carrying out a discrete-to-continuum variational analysis as the lattice spacing tends to zero, finding the energetic regime for which many chiral phases can coexist. In particular, we will show that the surface tension between the chiral phases is captured by a continuum energy obtained by suitably selecting solutions to the eikonal equation. The results presented in the seminar are based on works in collaboration with M. Cicalese and M. Forster.

Wed 26/04/23  |  16.00 - 17.00, Dipartimento di Matematica - Aula XII


Francesco Pepe (University of Bari)

Title: The many facets of quantum decay

Abstract: The exponential law, deriving from a classical statistical assumption, is extremely effective in describing the decay of many unstable quantum systems, such as the excited states of an atomic electron. However, such a law does not emerge naturally in the context of quantum mechanics, unless specific small-coupling requests are made, leading to the famous Fermi's "golden rule". Actually, quantum mechanics generally predicts non-exponential decay, at least for specific time ranges: the survival probability of an unstable state is characterized by an initial regime of quadratic decrease, while at large times it must follow, in a very wide range of physical systems, a power law, with possible superimposed oscillations. In this seminar, I will outline the general aspects of quantum decay, describing how all these features can be identified in the behavior of a semi-analytically solvable nearest-neigbor hopping model, and showing that the model parameters can be tuned in order to enhance the relevance of the quadratic and the power-law decay regimes, at the expense of the exponential law.

Wed 03/05/23  |  16.00 - 17.00 , Dipartimento di Matematica - Aula XII


Marco Bertola (Concordia University - Montreal)

Title: Anharmonic oscillators, Fekete points and a conjecture of Shapiro and Tater

Abstract: In this talk I will discuss the recent solution of a conjecture of Shapiro and Tater about the location of the zeroes  of discriminants for the secular equation of a particular anharmonic oscillator. It was a numerical observation that these zeroes form almost the same pattern as the poles of the rational solutions of the second Painlevé equation.  In our recent work (in progress) with T. Grava and E. C. Heredia we show how to quantify the similarity between the two patterns. In the process we also connect the eigenfunctions of the "Exactly Solvable" spectrum of a quartic anharmonic oscillator with "degenerate" orthogonal polynomials. This connection shows to be surprisingly fruitful and extends to more general situations, allowing to generalize the celebrated theorem of Stieltjes on the electrostatic interpretation of the zeroes of the classical orthogonal polynomials. 

Wed 24/05/23  |  16.00 - 17.00, Dipartimento di Matematica - Aula VII


Davide Lonigro (University of Bari)

Title: Singular perturbations of self-adjoint operators 

Abstract: Self-adjoint linear operators on Hilbert spaces play a fundamental role in quantum mechanics, in which all physical observables are to be uniquely associated with self-adjoint operators. When dealing with unbounded operators, the self-adjointness request is not trivial: a suitable domain prescription is required. As such, given a self-adjoint operator, it is not immediate to determine whether self-adjointness can be recovered, modulo a convenient domain choice, under the formal addition of a second term—a perturbation. The problem is particularly poignant for perturbations which are singular, that is, do not admit a direct interpretation as linear operators on a Hilbert space, like Dirac deltas.

In this mini-course I shall provide an introduction to singular perturbations of self-adjoint operators on Hilbert spaces, with a focus on their applications in nonrelativistic quantum mechanics. Starting with a general overview about the theory of self-adjoint extensions, I shall eventually address the rigorous description of rank-one singular perturbations, and how they affect the spectral properties of the perturbed operator; finally, I shall hint at an overview on the general case.

Calendar: 

Wed 17/05/23  | 14.30-16.30

Fri  19/05/23  | 14.30-16.30

Mon 29/05/23  |  14.30-16.30

Wed  31/05/23  |  14.30-16.30

Dipartimento di Matematica - Aula IX


Giuseppe De Nittis (Universidad Católica de Chile)

Title: The Magnetic Spectral Triple: Applications and Open Questions

Abstract: Since the early works by Bellissard, non-commutative geometry (NCG) has proved to be an excellent tool for the analysis of the quantum Hall effect (QHE), and more in general for the study of the topological phases of matter. The central object of the Bellissard's NCG for the QHE is a spectral triple designed to deal with tight-binding operators. In this talk we will present a new spectral triple suitable to treat continuous magnetic operators. We will show how the QHE in the continuous can be described inside this new NCG. Certain possible new applications, along with some related open questions, will be also presented. Joint work with: F. Belmonte & M. Sandoval.

Thu 06/07/23  |  10.30 - 11.30, Dipartimento di Matematica - Aula X