5/12/2022: Davide Fermi @ 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

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.

20/12/2022: Thematic Day @ Como

December 20, 2022, 11:15
Dipartimento di Scienza e Alta Tecnologia
Università dell’Insubria
Via Valleggio 11


  • 11:15 – Annalisa Panati
  • 12:00 – Markus Lange
  • 12:45 – Lunch Break
  • 14:45 – Andrea Mantile
  • 15:30 – Cristina Caraci
  • 16:15 – Closing

Titles and Abstracts

CARACI: Fluctuations of N-particle quantum dynamics around the Gross-Pitaevskii equation

We consider the quantum dynamics of N interacting bosons in the Gross-Pitaevskii regime. We obtain a norm-approximation for the many-body evolution of initial states exhibiting Bose-Einstein condensation in terms of a unitary Fock space evolution with a quadratic generator for the fluctuations. In addition, using this result, we provide the proof of a central limit theorem for the fluctuations of bounded one-particle observables. This is a joint work with Jakob Oldenburg and Benjamin Schlein.

MANTILE: Scattering theory with both regular and singular perturbations

We provide an asymptotic completeness criterion and a representation formula for the scattering matrix of a scattering couple (A,B), where both A and B are self-adjoint operators and B formally corresponds to adding to A two terms, one regular and the other singular. This abstract construction applies to perturbations of the free Laplacian with a Kato-Rellich potential and a singular part modelling boundary or interface conditions at the boundary of a open, bounded Lipschitz domain. We will possibly discuss applications of these models to classical scattering problems.

LANGE: Adiabatic Evolution of Low-Temperature Many-Body Systems

We consider the evolution of thermal equilibrium state of finite-range, many-body fermionic lattice models after introducing a weak and slowly varying time-dependent perturbation. Under suitable assumptions on the external driving, we derive a representation for the average of the evolution of local observables via a convergent expansion in the perturbation, for small enough temperatures. Convergence holds for a range of parameters that is uniform in the size of the system. As an application, the expansion allows to prove closeness of the time-evolved state to the instantaneous Gibbs state of the perturbed system, in the sense of expectation of local observables, at zero and at small temperatures. The proof is based on a rigorous version of the Wick rotation.

PANATI: Entropic Fluctuations in Quantum Two-time Measurement Framework

Non-equilibrium statistical mechanics has seen some impressive developments in the last three decades, thank to the pioneering works of Evans, Cohen, Morris and Searles on the violation of the second law, soon followed by the ground-breaking formulation of the Fluctuation Theorem by Gallavotti and Cohen for entropy fluctuation in the early nineties. Their work was by vast literature, both theoretical and experimental. The extension of these results to the quantum setting has turned out to be surprisingly challenging and it is still an undergoing effort. Kurchan’s seminal work (2000) showed the measurement role has to be taken in account, leading to the introduction of the so called two-time measurement statistics (also known as full counting statistics). However introducing this frameworks leads to surprising phenomena with no classical counterpart. In this talk, I will present some work in progress, where we attempt to introduce a quantum equivalent of Gallavotti-Cohen (steady) entropic functional and compare it with the Evans-Searls (transient) entropic functional. We show that, due to the invasive measurement role, the situation differs considerably to its classical counterpart.
Joint work with T. Benoist, L. Bruneau, V. Jakšic, C.A.Pillet.