13/07/2023: Diwakar Naidu @ UniMi

Thursday, July 13, 2023 - 15:00
Sala di Rappresentanza
Mathematics Department, University of Milan
Via Cesare Saldini 50, Milano, Italy

SPEAKER: Diwakar Naidu


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.

5/6/2023: Andreas Deuchert @ 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.

11/07/2023: Davide Lonigro @ 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 spinboson 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

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

24/11/2022: Luca Fresta @ 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

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.

12/12/2022: Vojkan Jakšić @ UniMi

December 12, 2022, 11:15
- Aula Dottorato, 1st floor -
Mathematics Department, University of Milan
Via Cesare Saldini 50, Milano, Italy

SPEAKER: Vojkan Jakšić (McGill University Montreal)


Some remarks on adiabatic time evolution and quasi-static processes in translation-invariant quantum systems

This talks concerns slowly varying, non-autonomous quantum dynamics of a translation invariant spin or fermion system on the lattice Z^d . This system is assumed to be initially in thermal equilibrium, and we consider realizations of quasi-static processes in the adiabatic limit. By combining the Gibbs variational principle with the notion of quantum weak Gibbs states, we will discuss a number of general structural results regarding such realizations.

This talk is based on a joint work with C-A Pillet and C. Tauber.

30/5/2022: Laurent Lafleche @ UniMi

May 30, 2022, 16:30 (non-standard time)
Sala di Rappresentanza
Mathematics Department, University of Milan
Via Cesare Saldini 50, Milano, Italy

SPEAKER: Laurent Lafleche (U Texas at Austin)


Semiclassical regularity and mean-field limit
with singular potentials

In this talk I will present several techniques and concepts used in the context of the mean-field and the classical limit allowing to go from the N -body Schrödinger equation with singular potential to the Hartree–Fock and Vlasov equations, linked to works in collaboration with Chiara Saffirio and Jacky Chong. At the level of the Vlasov–Poisson equation, typical mean-field techniques from quantum mechanics for pure states can be translated to a weak-strong stability estimate in L^1 for the Vlasov equation. Another weak-strong stability can be obtained for the difference of the square roots of the solutions in L^2. They allow to better understand the mean-field and semiclassical estimates. These estimates are weak-strong in the sense that they require only the regularity of one of the solutions. This requires the propagation of a semi-classical notion of regularity uniformly in N and h. A typical obstacle is the lack of positivity of the Wigner transform and its few conserved quantities. A solution to this problem is to consider operators as the right generalization of the phase space distribution, and a quantum analogue of Sobolev spaces defined using Schatten norms. The advantage of these techniques is that they allow to obtain regularity estimates without higher order error terms.

16/5/2022: Robin Reuvers @ UniMi

May 16, 2022, 16:30 (non-standard time)
Sala di Rappresentanza
Mathematics Department, University of Milan
Via Cesare Saldini 50, Milano, Italy

SPEAKER: Robin Reuvers (U Roma Tre)


Ground state energy of dilute Bose gases in 1D

In 1963, Lieb and Liniger formulated an exactly solvable model for interacting bosons in 1D. Thanks to its exact, Bethe ansatz solution, the model and its generalizations soon became popular objects of study in mathematical physics. Later, when new techniques allowed for the creation of (quasi-)1D systems in the lab, the Lieb-Liniger model found experimental use and became even better known.

In the meantime, Lieb and collaborators had moved on, and were rigorously studying interacting bosons in 2 and 3D. Without the availability of exact solutions, rigorous results were much more difficult to acquire, and a popular goal was the rigorous derivation of the ground state energy of gases of bosons in various settings in 2 and 3D. Many of the results focused on the dilute limit, in which the density of the boson gas is very low.

Somehow, Bose gases in 1D were excluded from this development. Of course, the original Lieb-Liniger model provided a solvable example, but we can nevertheless use insights from the 2 and 3D approaches to prove new results about the ground state energy of dilute Bose gases in 1D.

In the talk, I will review the developments above, and explain the new results.