  The conductance of a point contact between two hopping insulators is expected
to be dominated by the individual localized states in its vicinity. Here we
study the additional effects due to an external magnetic field. Combined with
the measured conductance, the measured magnetoresistance provides detailed
information on these states (e.g. their localization length, the energy
difference and the hopping distance between them). We also calculate the
statistics of this magnetoresistance, which can be collected by changing the
gate voltage in a single device. Since the conductance is dominated by the
quantum interference of particular mesoscopic structures near the point
contact, it is predicted to exhibit Aharonov-Bohm oscillations, which yield
information on the geometry of these structures. These oscillations also depend
on local spin accumulation and correlations, which can be modified by the
external field. Finally, we also estimate the mesoscopic Hall voltage due to
these structures.
