Stability and Absence of Binding for Multi-Polaron Systems

TL;DR

This paper proves the stability of multi-polaron systems and the absence of multi-particle binding for certain Coulomb repulsion strengths, resolving longstanding questions in polaron physics.

Contribution

It establishes conditions for stability and non-binding in multi-polaron models, including the Fröhlich and Pekar-Tomasevich models, based on Coulomb repulsion and coupling parameters.

Findings

Stability of matter holds for U > 2α.

No multi-particle binding occurs if U exceeds a critical value.

Thermodynamic limit of ground state energy per particle is finite for U > 2α.

Abstract

We resolve several longstanding problems concerning the stability and the absence of multi-particle binding for N\geq 2 polarons. Fr\"ohlich's 1937 polaron model describes non-relativistic particles interacting with a scalar quantized field with coupling \sqrt\alpha, and with each other by Coulomb repulsion of strength U. We prove the following: (i) While there is a known thermodynamic instability for U<2\alpha, stability of matter does hold for U>2\alpha, that is, the ground state energy per particle has a finite limit as N\to\infty. (ii) There is no binding of any kind if U exceeds a critical value that depends on \alpha but not on N. The same results are shown to hold for the Pekar-Tomasevich model.