62 citations · 335 across the 24 of their papers we have counts for
26 papers
Convergence of states for polaron models in the classical limit
Marco Falconi, Alessandro Olgiati, Nicolas Rougerie
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…
Renormalized Bogoliubov Theory for the Nelson Model
Marco Falconi, Jonas Lampart, Nikolai Leopold +1
We consider the time evolution of the renormalized Nelson model, which describes bosons linearly coupled to a quantized scalar field, in the mean-field limit of many particles…
Quasi-Classical Spin-Boson Models
Michele Correggi, Marco Falconi, Marco Merkli
In this short note we study Spin-Boson Models from the Quasi-Classical standpoint. In the Quasi-Classical limit, the field becomes macroscopic while the particles it interacts with…
Derivation of the Maxwell-Schrödinger Equations: A note on the infrared sector of the radiation field
Marco Falconi, Nikolai Leopold
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…
Entanglement Hamiltonians: from field theory, to lattice models and experiments
M. Dalmonte, V. Eisler, M. Falconi +1
We review results about entanglement (or modular) Hamiltonians of quantum many-body systems in field theory and statistical mechanics models, as well as recent applications in the…
Towards a derivation of Classical ElectroDynamics of charges and fields from QED
Zied Ammari, Marco Falconi, Fumio Hiroshima
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 agre…
Semiclassical analysis of quantum asymptotic fields in the Yukawa theory
Zied Ammari, Marco Falconi, Marco Olivieri
In this article, we study the asymptotic fields of the Yukawa particle-field model of quantum physics, in the semiclassical regime , with an interaction subject to an…
Bogoliubov Dynamics and Higher-order Corrections for the Regularized Nelson Model
Marco Falconi, Nikolai Leopold, David Mitrouskas +1
We study the time evolution of the Nelson model in a mean-field limit in which N non-relativistic bosons weakly couple (w.r.t. the particle number) to a positive or zero mass quant…
Ground State Properties in the Quasi-Classical Regime
Michele Correggi, Marco Falconi, Marco Olivieri
We study the ground state energy and ground states of systems coupling non-relativistic quantum particles and force-carrying Bose fields, such as radiation, in the quasi-classical…
The dilute Fermi gas via Bogoliubov theory
Marco Falconi, Emanuela L. Giacomelli, Christian Hainzl +1
We study the ground state properties of interacting Fermi gases in the dilute regime, in three dimensions. We compute the ground state energy of the system, for positive interactio…
Quasi-Classical Dynamics
M. Correggi, M. Falconi, M. Olivieri
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 excitati…
Microscopic Derivation of Time-dependent Point Interactions
R. Carlone, M. Correggi, M. Falconi +1
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…
On some rigorous aspects of fragmented condensation
Daniele Dimonte, Marco Falconi, Alessandro Olgiati
In this paper we discuss some aspects of fragmented condensation from a mathematical perspective. We first propose a simple way of characterizing finite fragmentation. Then, inspir…
Magnetic Schrödinger Operators as the Quasi-Classical Limit of Pauli-Fierz-type Models
M. Correggi, M. Falconi, M. Olivieri
We study the quasi-classical limit of the Pauli-Fierz model: the system is composed of finitely many non-relativistic charged particles interacting with a bosonic radiation field.…
Concentration of cylindrical Wigner measures
Marco Falconi
In this note we aim to characterize the cylindrical Wigner measures associated to regular quantum states in the Weyl C*-algebra of canonical commutation relations. In particular, w…
Effective Potentials Generated by Field Interaction in the Quasi-Classical Limit
Michele Correggi, Marco Falconi
We study the {\it quasi-classical limit} of a quantum system composed of finitely many non-relativistic particles coupled to a quantized field in Nelson-type models. We prove that,…
Cylindrical Wigner measures
Marco Falconi
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…
Bohr's correspondence principle in quantum field theory and classical renormalization scheme: the Nelson model
Zied Ammari, Marco Falconi
In the mid Sixties Edward Nelson proved the existence of a consistent quantum field theory that describes the Yukawa-like interaction of a non-relativistic nucleon field with a rel…
Scattering theory for Lindblad master equations
Marco Falconi, Jérémy Faupin, Jürg Fröhlich +1
We study scattering theory for a quantum-mechanical system consisting of a particle scattered off a dynamical target that occupies a compact region in position space. After taking…
On the rate of convergence for the mean field approximation of many-body quantum dynamics
Zied Ammari, Marco Falconi, Boris Pawilowski
We consider the time evolution of quantum states by many-body Schrödinger dynamics and study the rate of convergence of their reduced density matrices in the mean field limit. If t…
Self-Adjointness criterion for operators in Fock spaces
Marco Falconi
In this paper we provide a criterion of essential self-adjointness for operators in the tensor product of a separable Hilbert space and a Fock space. The class of operators we cons…
Wigner measures approach to the classical limit of the Nelson model: Convergence of dynamics and ground state energy
Zied Ammari, Marco Falconi
We consider the classical limit of the Nelson model, a system of stable nucleons interacting with a meson field. We prove convergence of the quantum dynamics towards the evolution…
Global Solution of the Electromagnetic Field-Particle System of Equations
Marco Falconi
In this paper we discuss global existence of the solution of the Maxwell and Newton system of equations, describing the interaction of a rigid charge distribution with the electrom…
Mean field limit of bosonic systems in partially factorized states and their linear combinations
Marco Falconi
We study the mean field limit of one-particle reduced density matrices, for a bosonic system in an initial state with a fixed number of particles, only a fraction of which occupies…