Repulsive Casimir interaction: Boyer oscillators at nanoscale

TL;DR

This paper investigates how temperature influences the repulsive Casimir force between permeable and polarizable plates, revealing a stable equilibrium configuration and introducing the concept of Boyer oscillators at the nanoscale.

Contribution

It introduces the Boyer oscillator model, demonstrating stable equilibrium and linear restoring forces in a Casimir system with temperature effects, advancing understanding of nanoscale quantum fluctuations.

Findings

Stable mechanical equilibrium exists with a permeable plate in the middle of two conductors.

Restoring force is linear with displacement, with a spring constant depending on temperature and separation.

Array of oscillators acts as an Einsteinian crystal with fluctuation forces from displacement.

Abstract

We study the effect of temperature on the repulsive Casimir interaction between an ideally permeable and an ideally polarizable plate {\it in vacuo}. At small separations or for low temperatures the quantum fluctuations of the electromagnetic field give the main contribution to the interaction, while at large separations or for high temperatures the interaction is dominated by the classical thermal fluctuations of the field. At intermediate separations or finite temperatures both the quantum and thermal fluctuations contribute. For a system composed of one infinitely permeable plate between two ideal conductors at a finite temperature, we identify a {\it stable mechanical equilibrium} state, if the infinitely permeable plate is located in the middle of the cavity. For small displacements the restoring force of this {\it Boyer oscillator} is linear in the deviation from the equilibrium position, with a spring constant that depends inversely on the separation between the two conducting plates and linearly on temperature. Furthermore, an array of such oscillators presents an ideal Einsteinian crystal that displays a fluctuation force between its outer boundaries stemming from the displacement fluctuations of the Boyer oscillators.