Exact Solutions to Non-Linear Symmetron Theory: One and Two Mirror Systems

TL;DR

This paper derives exact analytical solutions for symmetron field equations in one and two mirror systems, revealing a discrete set of solutions with multiple nodes, applicable to experimental physics setups like qBOUNCE and neutron interferometry.

Contribution

It provides the first exact solutions to symmetron equations in mirror systems, expressed via Jacobi elliptic functions, and uncovers multiple solutions with varying energies.

Findings

Solutions expressed in Jacobi elliptic functions.

Multiple solutions with increasing nodes and energies.

Applicable to experimental setups like qBOUNCE and Casimir force calculations.

Abstract

We derive the exact analytical solutions to the symmetron field theory equations in the presence of a one or two mirror system. The one dimensional equations of motion are integrated exactly for both systems and their solutions can be expressed in terms of Jacobi elliptic functions. Surprisingly, in the case of two parallel mirrors the equations of motion generically provide not a unique solution but a discrete set of solutions with increasing number of nodes and energies. The solutions obtained herein can be applied to qBOUNCE experiments, neutron interferometry and for the calculation of the symmetron field induced "Casimir force" in the CANNEX experiment.