Can spontaneous symmetry breaking occur in potential with one minima?

Abstract

Spontaneous symmetry breaking occurs when the symmetry that a physical system possesses, is not preserved for the ground state of the system. Although the procedure of symmetry breaking is quite clear from the mathematical point of view, the physical interpretation of the phenomenon is worth to be better understood. In this note we present a simple and instructive example of the symmetry breaking in a mechanical system. It demonstrates that the spontaneous symmetry breaking can occur for the spatially extended solutions in a potential characterised by a single minimum.