Quantum Spring

TL;DR

This paper reviews the concept of quantum spring, a Casimir effect with spring-like behavior in a helix boundary condition, highlighting its attractive forces and dependence on geometric ratios.

Contribution

It introduces the quantum spring effect derived from Casimir forces in helix geometries, expanding understanding of quantum boundary effects.

Findings

Force behaves like Hooke's law for small ratio r

Perpendicular force decreases monotonically with r

Behavior consistent in 2D and 3D

Abstract

In this paper, we will give a short review on \textit{quantum spring}, which is a Casimir effect from the helix boundary condition that proposed in our earlier works. The Casimir force parallel to the axis of the helix behaves very much like the force on a spring that obeys the Hooke's law when the ratio $r$ of the pitch to the circumference of the helix is small, but in this case, the force comes from a quantum effect, so we would like to call it \textit{quantum spring}. On the other hand, the force perpendicular to the axis decreases monotonically with the increasing of the ratio $r$. Both forces are attractive and their behaviors are the same in two and three dimensions.