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.

5/6/2023: Andreas Deuchert @ UniMi

quantumseminarSeminar 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.

25/05/2023: Hynek Kovarik @PoliMi

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

SPEAKER: Hynek Kovarik (Università degli studi di Brescia)

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.

11/07/2023: Davide Lonigro @ UniMi

Sascha LillSeminar 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 spin–boson 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

quantumseminarSeminar 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

20/02/2023: Jan Derezinski @ Polimi

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

SPEAKER: Jan Derezinski (University of Warsaw)

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.

5/12/2022: Davide Fermi @ PoliMi

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

SPEAKER: Davide Fermi (Politecnico di Milano)

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)

24/11/2022: Luca Fresta @ UniMi

quantumseminarSeminar 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.

21/11/2022: Nikolai Leopold @ UniMi

quantumseminarSeminar UniMi 
November 21, 2022, 11:15
Sala di Rappresentanza
Mathematics Department, University of Milan
Via Cesare Saldini 50, Milano, Italy

SPEAKER: Nikolai Leopold (Universität Basel)

Norm approximations for the Fröhlich dynamics

In this talk I will discuss recent results about the time evolution of the Fröhlich Hamiltonian in a mean-field limit in which many particles weakly couple to the quantized phonon field. For large particle number and initial data in which the particles are in a Bose-Einstein condensate and the excitations of the phonon field are in a coherent state I will show that the time evolved many-body state can be approximated in norm by an effective dynamics. The approximation is given by a product state which evolves according to the Landau–Pekar equations and which is corrected by a Bogoliubov dynamics.
If time permits I will, in addition, present a joint work with D. Mitrouskas, S. Rademacher, B. Schlein and R. Seiringer about the Fröhlich model in the strong coupling limit and compare the Bogoliubov dynamics in the strong coupling and mean-field regime.

Norm-approximations-for-the-Frohlich-dynamicsDownload