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 …

Quasi-classical dynamics

M Correggi, M Falconi, M Olivieri - Journal of the European …, 2022 - ems.press
We study quantum particles in interaction with a force-carrying field, in the quasi-classical
limit. This limit is characterized by the field having a very large number of excitations (it is …

Ground state properties in the quasiclassical regime

M Correggi, M Falconi, M Olivieri - Analysis & PDE, 2023 - msp.org
We study the ground state energy and ground states of systems coupling nonrelativistic
quantum particles and force-carrying Bose fields, such as radiation, in the quasiclassical …

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 …

Mean-field dynamics for the Nelson model with fermions

N Leopold, S Petrat - Annales Henri Poincaré, 2019 - Springer
We consider the Nelson model with ultraviolet cutoff, which describes the interaction
between non-relativistic particles and a positive or zero mass quantized scalar field. We take …

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 …

On the semiclassical regularity of thermal equilibria

JJ Chong, L Lafleche, C Saffirio - INdAM Meeting: Quantum Mathematics …, 2022 - Springer
We study the regularity properties of fermionic equilibrium states at finite positive
temperature and show that they satisfy certain semiclassical bounds. As a corollary, we …

Cylindrical wigner measures

M Falconi - Documenta Mathematica, 2018 - ems.press
In this paper we study the semiclassical behavior of quantum states acting on the C*-algebra
of canonical commutation relations, from a general perspective. The aim is to provide a …