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

@article{Correggi2017EffectivePG, title={Effective Potentials Generated by Field Interaction in the Quasi-Classical Limit}, author={Michele Correggi and Marco Falconi}, journal={Annales Henri Poincar{\'e}}, year={2017}, volume={19}, pages={189-235} }

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…

## 23 Citations

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. 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…

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- 2019

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- PhysicsAnnales Henri Poincaré
- 2019

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- 2018

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## References

SHOWING 1-10 OF 54 REFERENCES

### Partially Classical Limit of the Nelson Model

- Physics
- 2004

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

- Physics, Mathematics
- 1964

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

- Physics
- 2008

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

- Physics
- 2015

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

- Physics, Mathematics
- 2014

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

- Physics
- 2009

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

- Mathematics, Physics
- 1993

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

- Mathematics
- 2015

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

- Physics, Mathematics
- 2016

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

- Physics
- 2013

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…