Nonlinear (Anharmonic) Casimir Oscillator

TL;DR

This paper investigates the nonlinear dynamics of a micro spring influenced by the quantum Casimir force, revealing conditions for approximate sinusoidal oscillations that could help control stiction in micromechanical systems.

Contribution

It introduces an analysis of a nonlinear Casimir oscillator, identifying specific conditions for approximate solutions and potential applications in micromechanical device control.

Findings

Approximate sinusoidal solutions exist under specific conditions.

Turning points of the system are confined to small position intervals.

Potential application in mitigating Casimir stiction in microdevices.

Abstract

We want to study the dynamics of a simple linear harmonic micro spring which is under the influence of the quantum Casimir force/pressure and thus behaves as a (an) nonlinear (anharmonic) Casimir oscillator. Generally,the equation of motion of this nonlinear micromechanical Casimir oscillator has no exact solvable (analytical)solution and the turning point(s) of the system has (have) no fixed position(s); however, for particular values of the stiffness of the micro spring and at appropriately well-chosen distance scales and conditions, there is (are) approximately sinusoidal solution(s) for the problem (the variable turning points are collected in a very small interval of positions). This, as a simple and elementary plan, may be useful in controlling the Casimir stiction problem in micromechanical devices.