# Semiclassical analysis of quantum asymptotic fields in the Yukawa theory

@inproceedings{Ammari2021SemiclassicalAO, title={Semiclassical analysis of quantum asymptotic fields in the Yukawa theory}, author={Zied Ammari and Marco Falconi and Marco Olivieri}, year={2021} }

. In this article, we study the asymptotic ﬁelds of the Yukawa particle-ﬁeld model of quantum physics, in the semiclassical regime ℏ → 0, with an interaction subject to an ultraviolet cutoﬀ. We show that the transition amplitudes between ﬁnal (respectively initial) states converge towards explicit quantities involving the outgoing (respectively incoming) wave operators of the nonlinear Schr¨odinger–Klein–Gordon (S-KG) equation. Thus, we rigorously link the scattering theory of the Yukawa model…

## One Citation

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

- Physics
- 2022

. 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 ,…

## References

SHOWING 1-10 OF 45 REFERENCES

### Asymptotic Behavior of Solutions for the Coupled Klein–Gordon–Schrödinger Equations

- Physics, Mathematics
- 1994

Equations (1.1)-(1.2) describe a classical model ofYukawa's interaction of conserved complex nucleon field with neutral real meson field and the associated mass has been normalized as unity. Here…

### Mean-field limits of particles in interaction with quantized radiation fields

- Physics
- 2017

We report on a simple strategy to treat mean-field limits of quantum mechanical systems in which a large number of particles weakly couple to a second-quantized radiation field. Extending the method…

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

- Mathematics, PhysicsJournal of Spectral Theory
- 2019

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…

### Scattering Theory for the Coupled Klein-Gordon-Schrödinger Equations in Two Space Dimensions

- Mathematics
- 2003

We study the scattering theory for the coupled Klein- Gordon-Schrodinger equation with the Yukawa type interaction in two space dimensions.The scattering problem for this equation belongs to the…

### Asymptotic Electromagnetic Fields in Models of Quantum-Mechanical Matter Interacting with the Quantized Radiation Field

- Physics
- 2000

In models of (non-relativistic and pseudo-relativistic) electrons interacting with static nuclei and with the (ultraviolet-cutoff) quantized radiation field, the existence of asymptotic…

### Classical limit of the Nelson model with cutoff

- Physics, Mathematics
- 2013

In this paper we analyze the classical limit of the Nelson model with cutoff, when both non-relativistic and relativistic particles number goes to infinity. We prove convergence of quantum…

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

- PhysicsSIAM J. Math. Anal.
- 2020

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.

### 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…

### 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…