Effective Potentials Generated by Field Interaction in the Quasi-Classical Limit

  title={Effective Potentials Generated by Field Interaction in the Quasi-Classical Limit},
  author={Michele Correggi and Marco Falconi},
  journal={Annales Henri Poincar{\'e}},
We study the quasi-classical limit of a quantum system composed of finitely many nonrelativistic particles coupled to a quantized field in Nelson-type models. We prove that, as the field becomes classical and the corresponding degrees of freedom are traced out, the effective Hamiltonian of the particles converges in resolvent sense to a self-adjoint Schrödinger operator with an additional potential, depending on the state of the field. Moreover, we explicitly derive the expression of such a… 

Magnetic Schrödinger operators as the quasi-classical limit of Pauli–Fierz-type models

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. We trace out the

Microscopic Derivation of Time-dependent Point Interactions

We study the dynamics of the three-dimensional Frohlich polaron -- a quantum particle coupled to a bosonic field -- in the quasi-classical regime, i.e., when the field is very intense and the

Quasi-classical Ground States. II. Standard Model of Non-relativistic QED

. 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 the energy

Ground State Properties in the Quasi-Classical Regime

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 approximation. The

Quasi-classical Ground States. I. Linearly Coupled Pauli-Fierz Hamiltonians

. We consider a spinless, non-relativistic particle bound by an external potential and linearly coupled to a quantized radiation field. The energy E ( u, f ) of product states of the form u ⊗ Ψ f ,

Quasi-Classical Dynamics

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

Mean-Field Dynamics for the Nelson Model with Fermions

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 the

Derivation of the Maxwell-Schrödinger Equations from the Pauli-Fierz Hamiltonian

It is shown that at later times and in the limit of the mean-field limit the charged particles as well as the photons exhibit condensation, with the time evolution approximately described by the Maxwell-Schr\"odinger system, which models the coupling of a non-relativistic particle to the classical electromagnetic field.

Effective evolution equations from quantum mechanics

The goal of this thesis is to provide a mathematical rigorous derivation of the Schrodinger-Klein-Gordon equations, the Maxwell-Schrodinger equations and the defocusing cubic nonlinear Schrodinger

Norm approximation for the Fr\"ohlich dynamics in the mean-field regime

We study the time evolution of the Fr¨ohlich Hamiltonian in a mean-field limit in which many particles weakly couple to the quantized phonon field. Assuming that the particles are initially in a



Partially Classical Limit of the Nelson Model

Abstract.We consider the Nelson model which describes a quantum system of nonrelativistic identical particles coupled to a possibly massless scalar Bose field through a Yukawa type interaction. We

Interaction of Nonrelativistic Particles with a Quantized Scalar Field

We demonstrate the mathematical existence of a meson theory with nonrelativistic nucleons. A system of Schrodinger particles is coupled to a quantized relativistic scalar field. If a cutoff is put on

Effective Dynamics for Particles Coupled to a Quantized Scalar Field

We consider a system of N non-relativistic spinless quantum particles (“electrons”) interacting with a quantized scalar Bose field (whose excitations we call “photons”). We examine the case when the

Hamiltonian systems and semiclassical dynamics for interacting spins in QED

In this article, we consider fixed spin-1/2 particles interacting through the quantized electromagnetic field in a constant magnetic field. We give approximate evolutions of coherent states. This

Wigner Measures Approach to the Classical Limit of the Nelson Model: Convergence of Dynamics and Ground State Energy

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 of the coupled

Mean field limit for bosons and propagation of Wigner measures

We consider the N-body Schrodinger dynamics of bosons in the mean field limit with a bounded pair-interaction potential. According to the previous work [Ammari, Z. and Nier, F., “Mean field limit for

Scaling limit of a model of quantum electrodynamics

This article gives a solution to an open problem in the paper by Arai [J. Math. Phys. 31, 2653 (1990)]. In it is presented an abstract asymptotic theory of families of unitary operators {U(κ)}κ≳0 and

Self-adjointness and domain of the Fröhlich Hamiltonian

In the large polaron model of Herbert Frohlich, the electron-phonon interaction is a small perturbation in form sense, but a large perturbation in operator sense. This means that the form-domain of

On the dynamics of polarons in the strong-coupling limit

The polaron model of H. Frohlich describes an electron coupled to the quantized longitudinal optical modes of a polar crystal. In the strong-coupling limit, one expects that the phonon modes may be

Semiclassical polaron dynamics of impurities in ultracold gases

We present a semiclassical treatment of a fermionic impurity coupled to Bogolyubov modes of a Bose-Einstein condensate (BEC). In the lowest-order approximation we find a full solution of an initial