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

TL;DR

This paper derives exact analytical solutions for the symmetron field equations in one and two mirror systems, enhancing understanding of symmetron behavior in different phases and aiding experimental applications.

Contribution

It provides the first exact solutions for symmetron fields in mirror systems with broken phases, expressed via Jacobi elliptic functions, extending previous work.

Findings

Exact solutions in terms of Jacobi elliptic functions

Discrete set of solutions with increasing nodes and energies for two mirrors

Applications to qBOUNCE, neutron interferometry, 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 in the case of a spontaneously broken phase in vacuum as well as in matter. This complements a similar analysis performed in a previous article [1], in which the symmetron is in the spontaneously broken phase in vacuum but in the symmetric phase in matter. Here again, the one dimensional equations of motion are integrated exactly for both systems and their solutions are expressed in terms of Jacobi elliptic functions. In the case of two parallel mirrors the equations of motion provide also in this case 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 to the calculation of the symmetron field induced "Casimir force" in the Cannex experiment and allow to extend the investigation to hitherto unavailable regions in symmetron parameter space.