  Within a Ginzburg-Landau formalism we establish analytically the necessary
and sufficient conditions to realize a doubly degenerate superconducting ground
state with broken time-reversal symmetry (BTRS) in a multi-band superconductor.
Using these results we analyze the ground state of a three-band superconductor
in the cylindrical geometry in an external magnetic field. We show that
depending on the interband coupling constants, a magnetic flux can induce
current density jumps in such superconducting geometries that are related to
adiabatic or non-adiabatic transitions from BTRS to time-reversal symmetric
states and vice versa. This unusual current induced magnetic flux response can
in principle be used experimentally to detect superconducting BTRS ground
states as well as corresponding metastable excited states.
