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.

26/10/2022: Jérémy Faupin @ PoliMi

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

SPEAKER: Jérémy Faupin (U de Lorraine @Metz)

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.