Category: Seminar 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)

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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.

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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.

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)

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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.

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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.

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

SPEAKER: Angelo Lucia (Universidad Complutense de Madrid)

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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.

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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.

May 25, 2023 - 14h30
Aula Seminario III Piano, Politecnico di Milano
Edificio 14 (Nave), Campus Leonardo

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SPEAKER: Hynek Kovarik (Università degli studi di Brescia)

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Resolvent expansion and time decay of the wave functions of magnetic Hamiltonians in dimension two

I this talk I will present some results on the resolvent expansions of magnetic Hamiltonians at the threshold of the essential spectrum. I will show, in particular, that the nature of the expansion of a two-dimensional magnetic Hamiltonian is completely determined by the flux of the associated magnetic field. Applications to time decay of the wave functions will be discussed as well.

February 20, 2023
Aula Consiglio VII Piano, Politecnico di Milano
Edificio 14 (Nave), Campus Leonardo

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SPEAKER: Jan Derezinski (University of Warsaw)

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Schrödinger operators with singular boundary conditions

In order to define a differential operator on a domain with boundary one often needs to specify boundary conditions. In the presence of singular terms this can be quite tricky. It may lead to interesting and surprising phase diagrams. I will illustrate this with the so-called perturbed Bessel operators, that is one-dimensional Schrödinger operators on the half-line of the form $ – \partial_x^2 + (m^2 – 1/4) 1/x^2 + Q(x) $.

The talk will be based on my joint work with Jeremy Faupin.

December 5, 2022
Aula Seminario VI Piano, Politecnico di Milano
Edificio 14 (Nave), Campus Leonardo

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SPEAKER: Davide Fermi (Politecnico di Milano)

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Vacuum fluctuations with zero-range potentials

The Casimir effect is a manifestation of van der Waals polarization forces
acting between atoms and molecules, in a regime where relativistic retardation
effects cannot be neglected. An effective description can be given in terms of
quantum fields influenced by classical objects, such as boundaries or external
potentials. This leads to the emergence of ultraviolet divergences which can be
treated by means of the so-called zeta-function regularization. In this seminar
I first present a rigorous implementation of the zeta-function technique, using
the language of canonical quantization for a scalar field. To this purpose,
complex powers of the elliptic operator describing the dynamics are used to
define smeared versions of the Wightman field and renormalization of
expectation values is ultimately attained by analytic continuation. Next, I
address the issue of boundary anomalies, discussing some explicitly solvable
models with zero-range potentials modeling semi-transparent walls.

Based on joint works with Livio Pizzocchero (University of Milano)

October 26, 2022, 11:15 (new time this semester)
Aula Seminario - III piano
Politecnico di Milano
Edificio 14 (Nave), Campus Leonardo
P.zza da Vinci 32, Milano, Italy

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SPEAKER: Jérémy Faupin (U de Lorraine @Metz)

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Quasi-classical ground states in non-relativistic QED and related models

We will consider in this talk a non-relativistic particle bound by an external
potential and coupled to a quantized radiation field. This physical system is
mathematically described by a Pauli-Fierz Hamiltonian. We will study the energy
functional of product states of the form u⊗Ψ_f, where u is a normalized state
for the non-relativistic particle and Ψ_f is a coherent state in Fock space for
the field. This gives the energy of a Klein-Gordon-Schrödinger system in the
case of a spinless particle linearly coupled to a scalar field, or the energy
of a Maxwell-Schrödinger system in the case of an electron coupled to the
photon field. In both cases, we will discuss results concerning the existence
and uniqueness of a ground state, under general conditions on the external
potential and the coupling form factor. In particular, neither an ultraviolet
cutoff nor an infrared cutoff needs to be imposed. We will also discuss the
convergence in the ultraviolet limit and the second-order asymptotic expansion
in the coupling constant of the ground state energy.
This is joint work with J. Payet and S. Breteaux.

For more information, go to https://sites.google.com/view/iqm22/workshop-ii

For more information, go to https://sites.google.com/view/iqm22/workshop-i

December 13, 2021, 14:00
Sala Consiglio - VII Piano
Politecnico di Milano
Building 14 (Nave), Campus Leonardo
P.zza da Vinci 32, Milano, Italy

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SPEAKER: Riccardo Adami (Politecnico di Torino)

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Ground states for the two-dimensional NLS in the presence of point interactions

We prove the existence of ground states, i.e. minimizers of the energy at fixed mass, for the focusing, subcritical Nonlinear Schroedinger equation in two dimensions, with a linear point interaction, or defect. Ground states turn out to be positive up to a phase, and to show a logaritmico singularity at the defect. The analogous problem has been widely treated in the one dimensional setting, including the case of graphs. The two dimensional version is more complicated because of the structure of the energy space, that is larger than the standard one. This result opens the way to the study of nonlinear hybrids. This is a joint work with Filippo Boni, Raffaele Carlone, and Lorenzo Tentarelli.

Important Notice: To access the seminar room, please wait at the entrance of the Mathematics Department, Building 14. One of the organizers will let you in using the dedicated elevator for staff. As per internal regulations of Politecnico, the COVID19 green certificate will be checked before entering the room.