# The polaron at strong coupling

@article{Seiringer2019ThePA,
title={The polaron at strong coupling},
author={Robert Seiringer},
journal={arXiv: Mathematical Physics},
year={2019}
}
• R. Seiringer
• Published 28 December 2019
• Physics
• arXiv: Mathematical Physics
We review old and new results on the Fr\"ohlich polaron model. The discussion includes the validity of the (classical) Pekar approximation in the strong coupling limit, quantum corrections to this limit, as well as the divergence of the effective polaron mass.
8 Citations
Ground state of the polaron hydrogenic atom in a strong magnetic field
The ground-state electron density of a polaron bound to a Coulomb potential in a homogeneous magnetic field--the transverse coordinates integrated out--converges pointwise and weakly in the strong
Impurity immersed in a double Fermi sea
• Physics, Computer Science
Physical Review A
• 2020
It is shown that in the strong-coupling regime, the system undergoes a first order transition between polaronic and trimer states, suggesting that the smooth crossover predicted for a superfluid background is the consequence of Cooper pairing and is absent in a normal system.
Landau–Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron
• Physics
Pure 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
The Fr\"ohlich Polaron at Strong Coupling -- Part I: The Quantum Correction to the Classical Energy
• Physics
• 2022
. We study the Fr¨ohlich polaron model in R 3 , and establish the subleading term in the strong coupling asymptotics of its ground state energy, corresponding to the quantum corrections to the
Principle and Applications of Multimode Strong Coupling Based on Surface Plasmons
• Physics
Nanomaterials
• 2022
In the past decade, strong coupling between light and matter has transitioned from a theoretical idea to an experimental reality. This represents a new field of quantum light–matter interaction,
The effective mass problem for the Landau–Pekar equations
• Physics
Journal of Physics A: Mathematical and Theoretical
• 2021
We provide a definition of the effective mass for the classical polaron described by the Landau–Pekar (LP) equations. It is based on a novel variational principle, minimizing the energy functional
The Strongly Coupled Polaron on the Torus: Quantum Corrections to the Pekar Asymptotics
• Physics, Mathematics
Archive for Rational Mechanics and Analysis
• 2021
We investigate the Fröhlich polaron model on a three-dimensional torus, and give a proof of the second-order quantum corrections to its ground-state energy in the strong-coupling limit. Compared to
Quantum dynamics of a Bose polaron in a d -dimensional Bose-Einstein condensate
• Physics
• 2021
We study the quantum motion of an impurity atom immersed in a Bose-Einstein condensate in arbitrary dimensions. It was shown, for all dimensions, that the Bogoliubov excitations of the Bose-Einstein

## References

SHOWING 1-10 OF 49 REFERENCES
Divergence of the Effective Mass of a Polaron in the Strong Coupling Limit
• Physics
Journal of statistical physics
• 2020
The Fröhlich model of a polaron is considered, and it is shown that its effective mass diverges in the strong coupling limit.
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
Quantum Corrections to the Pekar Asymptotics of a Strongly Coupled Polaron
• Physics, Mathematics
Communications on Pure and Applied Mathematics
• 2020
We consider the Fröhlich polaron model in the strong coupling limit. It is well‐known that to leading order the ground state energy is given by the (classical) Pekar energy. In this work, we
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
Exact Ground State Energy of the Strong-Coupling Polaron
• Mathematics
• 1995
Abstract: The polaron has been of interest in condensed matter theory and field theory for about half a century, especially the limit of large coupling constant, α. It was not until 1983, however,
Effective Mass of the Polaron—Revisited
• Mathematics, Physics
• 2019
Properties of the energy–momentum relation for the Fröhlich polaron are of continuing interest, especially for large values of the coupling constant. By combining spectral theory with the available
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
Ground state properties of multi-polaron systems
• Physics
• 2012
We summarize our recent results on the ground state energy of multi-polaron systems. In particular, we discuss stability and existence of the thermodynamic limit, and we discuss the absence of
Advances in Polaron Physics
• Physics
• 2009
Continuum Polaron.- Lattice Polaron.- Bipolaron.- Multipolaron Problem.- Polarons and Bipolarons in Advanced Materials.- Current Status of Polarons and Open Problems.