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

Understand

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.