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.