J. Berger, Spontaneous breaking of axial symmetry for the Schrodinger equation in thepresence of a magnetic field - art. no. 172507, PHYS REV B, 6317(17), 2001, pp. 2507
Symmetry breaking is a situation which is searched for in almost every bran
ch of science, since it allows for a regime in which the system under study
exhibits new properties. We have found a range in the (magnetic field)-(co
upling parameter) plane where the ground state for the Schrodinger and Ampe
re coupled equations in a cylindric domain does not have axial symmetry.