# Microscopic Derivation of Time-dependent Point Interactions

@article{Carlone2019MicroscopicDO, title={Microscopic Derivation of Time-dependent Point Interactions}, author={Raffaele Carlone and Michele Correggi and Marco Falconi and Marco Olivieri}, journal={arXiv: Mathematical Physics}, year={2019} }

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 corresponding degrees of freedom can be treated semiclassically. We prove that in such a regime the effective dynamics for the quantum particles is approximated by the one generated by a time-dependent point interaction, i.e., a singular time-dependent perturbation of the Laplacian supported in a point. As…

## 6 Citations

Complete ionization for a non-autonomous point interaction model in d = 2

- Mathematics
- 2021

We consider the two dimensional Schrödinger equation with time dependent delta potential, which represents a model for the dynamics of a quantum particle subject to a point interaction whose strength…

Bogoliubov Dynamics and Higher-order Corrections for the Regularized Nelson Model

- Mathematics
- 2021

We study the time evolution of the Nelson model in a mean-field limit in which N nonrelativistic bosons weakly couple (w.r.t. the particle number) to a positive or zero mass quantized scalar field.…

Ground State Properties in the Quasi-Classical Regime

- Physics
- 2020

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…

Derivation of the Landau–Pekar Equations in a Many-Body Mean-Field Limit

- PhysicsArchive for rational mechanics and analysis
- 2021

The Fröhlich Hamiltonian is considered in a mean-field limit where many bosonic particles weakly couple to the quantized phonon field and it is shown that the dynamics of the system is approximately described by the Landau–Pekar equations.

Landau–Pekar equations and quantum
fluctuations for the dynamics of a strongly coupled polaron

- PhysicsPure and Applied Analysis
- 2021

We consider the Frohlich Hamiltonian with large coupling constant $\alpha$. For initial data of Pekar product form with coherent phonon field and with the electron minimizing the corresponding…

Quasi-Classical Dynamics

- Physics
- 2019

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…

## References

SHOWING 1-10 OF 57 REFERENCES

Two-dimensional Time-dependent Point Interactions

- Mathematics, Physics
- 2016

We study the time-evolution of a quantum particle subjected to timedependent zero-range forces in two dimensions. After establishing a conceivable ansatz for the solution to the Schrödinger equation,…

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

- Mathematics, Physics
- 2017

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…

Ionization for Three Dimensional Time-Dependent Point Interactions

- Mathematics
- 2005

We study the time evolution of a three dimensional quantum particle under the action of a time-dependent point interaction fixed at the origin. We assume that the “strength” of the interaction α(t)…

Schrodinger Equation with Moving Point Interactions in Three Dimensions

- Mathematics
- 1999

We consider the motion of a non relativistic quantum particle in R^3 subject to n point interactions which are moving on given smooth trajectories. Due to the singular character of the time-dependent…

Rotating Singular Perturbations of the Laplacian

- Mathematics
- 2003

Abstract.
We study a system of a quantum particle interacting with a singular time-dependent
uniformly rotating potential in 2 and 3 dimensions: in particular we
consider an interaction with support…

The classical field limit of scattering theory for non-relativistic many-boson systems. II

- Physics, Mathematics
- 1979

We study the classical field limit of non relativistic many-boson theories in space dimensionn≧3, extending the results of a previous paper to more singular interactions. We prove the expected…

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…

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…

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…

Quantum Fluctuations and Rate of Convergence Towards Mean Field Dynamics

- Mathematics, Physics
- 2007

The nonlinear Hartree equation describes the macroscopic dynamics of initially factorized N-boson states, in the limit of large N. In this paper we provide estimates on the rate of convergence of the…