  The effects of the coupling between two electronic condensates in two-gap
mesoscopic superconductors are studied within the Ginzburg-Landau theory using
a finite difference technique. In applied magnetic field, we derive the
dependency of the size of the vortex on the sample size and the strength of the
Josephson coupling. In addition, we elaborate on the dependence of the critical
temperature and field on the parameters of the coupled condensates. We
demonstrate further the existence and stability of fractional states, for which
the two condensates comprise different vorticity. Moreover, we also found
pronounced asymmetric fractional states and we show their experimentally
observable magnetic response. Finally we introduce the magnetic coupling
between condensates, and study in particular the case where one band is type II
and the other is type I, i.e. the sample is effectively of I.x type. The
calculated M(H) loops show a clear signature of the mixed type of
superconductivity, which we find to be strongly affected by the ratio of the
coherence lengths in the two condensates.

Superconductivity