The ground state energy of a polaron in a strong magnetic field

TL;DR

This paper demonstrates that the ground state energy of a polaron in a strong magnetic field can be effectively described by a one-dimensional minimization problem, applicable to both linear and nonlinear models, as the magnetic field strength approaches infinity.

Contribution

It rigorously establishes the reduction to a one-dimensional problem for the polaron ground state energy in strong magnetic fields, extending previous heuristic arguments.

Findings

Effective 1D minimization describes the ground state energy as B→∞

Applicable to both Fröhlich and Pekar models

Provides rigorous justification for previous heuristic approaches

Abstract

We show that the ground state of a polaron in a homogeneous magnetic field $B$ and its energy are described by an effective one-dimensional minimization problem in the limit $B\to\infty$. This holds both in the linear Fr\"ohlich and in the non-linear Pekar model and makes rigorous an argument of Kochetov, Leschke and Smondyrev.