  We study a system of two quantum dots connected by a hopping bridge. Both the
dots and connecting region are assumed to be in universal crossover regimes
between Gaussian Orthogonal and Unitary ensembles. Using a diagrammatic
approach appropriate for energy separations much larger than the level spacing
we obtain the ensemble-averaged one- and two-particle Green's functions. It
turns out that the diffuson and cooperon parts of the two-particle Green's
function can be described by separate scaling functions. We then use this
information to investigate a model interacting system in which one dot has an
attractive s-wave reduced Bardeen-Cooper-Schrieffer interaction, while the
other is noninteracting but subject to an orbital magnetic field. We find that
the critical temperature is {\it nonmonotonic} in the flux through the second
dot in a certain regime of interdot coupling. Likewise, the fluctuation
magnetization above the critical temperature is also nonmonotonic in this
regime, can be either diamagnetic or paramagnetic, and can be deduced from the
cooperon scaling function.

Mesoscale and Nanoscale Physics