Ground state energy of large polaron systems

TL;DR

This paper determines the asymptotic behavior of the ground state energy for large bosonic polaron systems with Coulomb repulsion, providing bounds that closely match, thus solving a longstanding problem in the Pekar-Tomasevich approximation.

Contribution

It establishes the precise asymptotic scaling of the ground state energy for large systems and offers tight bounds on the asymptotic coefficient in the neutral case.

Findings

Ground state energy scales as -N^{7/5} for large N

Provided upper and lower bounds on the asymptotic coefficient

Solved a longstanding open problem in many-polaron systems

Abstract

The last unsolved problem about the many-polaron system, in the Pekar-Tomasevich approximation, is the case of bosons with the electron-electron Coulomb repulsion of strength exactly 1 (the 'neutral case'). We prove that the ground state energy, for large $N$, goes exactly as $-N^{7/5}$, and we give upper and lower bounds on the asymptotic coefficient that agree to within a factor of $2^{2/5}$.