Thermal Ionization for Short-Range Potentials

TL;DR

This paper demonstrates that a quantum particle in a short-range potential coupled to a thermal bosonic field undergoes thermal ionization at any positive temperature when the coupling is weak, using advanced mathematical methods.

Contribution

It provides a rigorous proof of thermal ionization for short-range potentials at positive temperatures, employing positive commutator techniques without unnatural restrictions.

Findings

Thermal ionization occurs at all positive temperatures for small coupling.

The model's analysis relies on positive commutator methods with dilations.

The proof uses a spatial cutoff in the coupling, avoiding unnatural restrictions.

Abstract

We study a concrete model of a confined particle in form of a Schr\"odinger operator with a compactly supported smooth potential coupled to a bosonic field at positive temperature. We show, that the model exhibits thermal ionization for any positive temperature, provided the coupling is sufficiently small. Mathematically, one has to rule out that zero is an eigenvalue of the self-adjoint generator of time evolution - the Liouvillian. This will be done by using positive commutator methods with dilations in the space of scattering functions. Our proof relies on a spatial cutoff in the coupling but does otherwise not require any unnatural restrictions.