Casimir-Polder intermolecular forces in minimal length theories

TL;DR

This paper investigates how minimal length theories modify Casimir-Polder forces, revealing a new attractive potential scaling as r^{-9} instead of the traditional r^{-7} at long ranges.

Contribution

It derives the first order correction to Casimir-Polder interactions due to minimal length effects, showing a different power-law behavior.

Findings

The correction introduces an attractive potential scaling as r^{-9}.

Minimal length effects alter the long-range behavior of intermolecular forces.

The study provides a theoretical foundation for minimal length impacts on quantum forces.

Abstract

Generalized uncertainty relations are known to provide a minimal length $\hbar\sqrt{\beta}$. The effect of such minimal length in the Casimir-Polder interactions between neutral atoms (molecules) is studied. The first order correction term in the minimal uncertainty parameter is derived and found to describe an attractive potential scaling as $r^{-9}$ as opposed to the well known $r^{-7}$ long range retarded potential.