# On the dynamics of the mean-field polaron in the high-frequency limit

@article{Griesemer2017OnTD, title={On the dynamics of the mean-field polaron in the high-frequency limit}, author={Marcel Griesemer and Jochen Schmid and Guido Schneider}, journal={Letters in Mathematical Physics}, year={2017}, volume={107}, pages={1809-1821} }

We consider the dynamics of the mean-field polaron in the limit of infinite phonon frequency $$\omega \rightarrow \infty $$ω→∞. This is a singular limit formally leading to a Schrödinger–Poisson system that is equivalent to the nonlinear Choquard equation. By establishing estimates between the approximation obtained via the Choquard equation and true solutions of the original system we show that the Choquard equation makes correct predictions about the dynamics of the polaron mean-field model…

## 3 Citations

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…

The Dirac-Klein-Gordon system in the strong coupling limit

- Mathematics, Physics
- 2021

We study the Dirac equation coupled to scalar and vector Klein-Gordon fields in the limit of strong coupling and large masses of the fields. We prove convergence of the solutions to those of a cubic…

Effective Slow Dynamics Models for a Class of Dispersive Systems

- Mathematics, Computer ScienceJournal of Dynamics and Differential Equations
- 2019

The abstract approximation theorem applies to a number of semilinear systems, such as the Dirac–Klein–Gordon system, the Klein–Gordon–Zakharov system, and a mean field polaron model.

## References

SHOWING 1-10 OF 21 REFERENCES

Dynamics of a Strongly Coupled Polaron

- Physics
- 2014

We study the dynamics of large polarons described by the Fröhlich Hamiltonian in the limit of strong coupling. The initial conditions are (perturbations of) product states of an electron wave…

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…

Derivation of the nonlinear Schr\"odinger equation from a many body Coulomb system

- Mathematics, Physics
- 2001

We consider the time evolution of N bosonic particles interacting via a mean field Coulomb potential. Suppose the initial state is a product wavefunction. We show that at any finite time the…

On the Point-Particle (Newtonian) Limit¶of the Non-Linear Hartree Equation

- Physics, Mathematics
- 2002

Abstract: We consider the nonlinear Hartree equation describing the dynamics of weakly interacting non-relativistic Bosons. We show that a nonlinear Møller wave operator describing the scattering of…

On the time evolution of the mean-field polaron

- Mathematics
- 2000

In this paper a mean-field theory for the evolution of an electron in a crystal is proposed in the framework of the Schrodinger formalism. The well-posedness of the problem as well as the…

Derivation of an effective evolution equation for a strongly coupled polaron

- Physics
- 2017

Frohlich’s polaron Hamiltonian describes an electron coupled to the quantized phonon field of an ionic crystal. We show that in the strong coupling limit the dynamics of the polaron are approximated…

Fröhlich polaron and bipolaron: recent developments

- Physics
- 2009

It is remarkable how the Frohlich polaron, one of the simplest examples of a Quantum Field Theoretical problem, as it basically consists of a single fermion interacting with a scalar Bose field of…

On a class of non linear Schrödinger equations with non local interaction

- Mathematics
- 1980

As regards the first question we prove existence and uniqueness of the solutions of the Cauchy problem with finite initial time; as regards the second one, we prove the existence of solutions of the…

The NLS Approximation Makes Wrong Predictions for the Water Wave Problem in Case of Small Surface Tension and Spatially Periodic Boundary Conditions

- Mathematics
- 2015

The nonlinear Schrödinger (NLS) equation describes small modulations in time and space of a spatially and temporally oscillating wave packet advancing in a laboratory frame. It has first been derived…

Validity and Limitation of the Newell‐Whitehead Equation

- Physics
- 1995

Modulation equations play an essential role in the description of systems which exhibit patterns of nearly periodic nature, e.g. in Benard's problem. The so called Newell-Whithead equation is derived…