Scaling limits of bosonic ground states, from many-body to non-linear Schrödinger

N Rougerie - EMS Surveys in Mathematical Sciences, 2021 - ems.press
How and why could an interacting system of many particles be described as if all particles
were independent and identically distributed? This question is at least as old as statistical …

Bogoliubov dynamics and higher-order corrections for the regularized Nelson model

M Falconi, N Leopold, D Mitrouskas… - Reviews in Mathematical …, 2023 - World Scientific
We study the time evolution of the Nelson model in a mean-field limit in which N
nonrelativistic bosons weakly couple (with respect to the particle number) to a positive or …

Quasi-classical ground states. I. Linearly coupled Pauli–Fierz Hamiltonians

S Breteaux, J Faupin, J Payet - Documenta Mathematica, 2023 - ems.press
Quasi-classical ground states. I. Linearly coupled Pauli–Fierz Hamiltonians Page 1 Doc. Math.
28 (2023), 1191–1233 DOI 10.4171/DM/929 © 2023 Deutsche Mathematiker-Vereinigung …

Towards a derivation of Classical ElectroDynamics of charges and fields from QED

Z Ammari, M Falconi, F Hiroshima - arXiv preprint arXiv:2202.05015, 2022 - arxiv.org
The purpose of this article is twofold. On one hand, we rigorously derive the Newton--
Maxwell equation in the Coulomb gauge from first principles of quantum electrodynamics in …

Quasi-classical ground states. II. Standard model of non-relativistic QED

S Breteaux, J Faupin, J Payet - arXiv preprint arXiv:2210.03448, 2022 - arxiv.org
We consider a non-relativistic electron bound by an external potential and coupled to the
quantized electromagnetic field in the standard model of non-relativistic QED. We compute …

Quasi-classical Limit of a Spin Coupled to a Reservoir

M Correggi, M Falconi, M Fantechi, M Merkli - arXiv preprint arXiv …, 2024 - arxiv.org
A spin (qubit) is in contact with a bosonic reservoir. The state of the reservoir contains a
parameter {\varepsilon} interpolating between quantum and classical reservoir features. We …

Emergence of time-dependent point interactions in polaron models

R Carlone, M Correggi, M Falconi, M Olivieri - SIAM Journal on Mathematical …, 2021 - SIAM
We study the dynamics of the three-dimensional polaron---a quantum particle coupled to
bosonic fields---in the quasi-classical regime. In this case, the fields are very intense and the …

[HTML][HTML] Derivation of the Maxwell–Schrödinger equations: A note on the infrared sector of the radiation field

M Falconi, N Leopold - Journal of Mathematical Physics, 2023 - pubs.aip.org
We slightly extend prior results about the derivation of the Maxwell–Schrödinger equations
from the bosonic Pauli–Fierz Hamiltonian. More concretely, we show that the findings from …

Convergence of states for polaron models in the classical limit

M Falconi, A Olgiati, N Rougerie - arXiv preprint arXiv:2311.05940, 2023 - arxiv.org
We consider the quasi-classical limit of Nelson-type regularized polaron models describing
a particle interacting with a quantized bosonic field. We break translation-invariance by …

Abstract semiclassical analysis of the van Hove model

M Falconi, L Fratini - arXiv preprint arXiv:2407.20603, 2024 - arxiv.org
In this paper we study the semiclassical limit $\hslash\to 0$ of a completely solvable model
in quantum field theory: the van Hove model, describing a scalar field created and …