Distinguishing models of surface response through the self-energy of an electron

TL;DR

This paper calculates the electron's self-energy near surfaces with different dielectric properties, revealing model-dependent sign differences that could be experimentally tested to clarify the correct surface response model.

Contribution

It introduces a general formula for the surface-dependent electron self-energy and compares predictions of the plasma and Drude models, proposing an experiment to distinguish between them.

Findings

Self-energy sign differs between plasma and Drude models.

Derived a general formula for surface-induced electron self-energy.

Proposed an experiment to test the model-dependent sign difference.

Abstract

The self-energy of an electron confined between parallel surfaces with arbitrary dielectric properties is calculated. The mechanism for this effect is the surface-induced modification of the fluctuating quantised vacuum field to which the electron is coupled, thereby endowing it with a surface-dependent self-energy in broad analogy to the Casimir-Polder effect for an atom. We derive a general formula for this self-energy shift and find that its sign is different for two commonly-used models of surface response, namely the plasma model and the Drude model. We propose an experiment which could detect this difference in sign, shedding light on continuing uncertainty about the correct description of the interaction of low-frequency vacuum photons with media.