Oscillating Casimir force of trapped Bose gas in electromagnetic field

TL;DR

This paper investigates the oscillating Casimir force in a trapped, charged Bose gas under electromagnetic fields, deriving analytical expressions and revealing force oscillations dependent on plate separation.

Contribution

It provides an analytical derivation of the Casimir potential and force for a charged Bose gas in electromagnetic fields, highlighting oscillatory behavior at the condensation temperature.

Findings

Casimir force oscillates with plate separation.

Analytical expressions for grand canonical potential derived.

Force behavior characterized at Bose-Einstein condensation temperature.

Abstract

In this study, we consider motion of the massive and charged Bose gas trapped in electric and magnetic fields between two parallel plates in the $x-y$ plane that are separated by a distance $d$ in the $z$ direction. We derive analytical expression of the grand canonical potential of the quantum particles by using of Ketterle and van Druten approximation. By evaluating canonical potential, we obtain Casimir potential and force at the Bose-Einstein condensation temperature $T_{c}$. We also show that Casimir force oscillates depends on distance $d$ for fixed parameters.