  The dependence of mesoscopic conductance fluctuations on parallel magnetic
field is used as a probe of spin degeneracy in open GaAs quantum dots. The
variance of fluctuations at high parallel field is reduced from the low-field
variance (with broken time-reversal symmetry) by factors ranging from roughly
two in a 1 square-micron dot at low temperature, to four or greater in 8
square-micron dots. The factor of two is expected for simple Zeeman splitting
of spin degenerate channels. A possible explanation for the unexpected larger
factors in terms of field-dependent spin orbit scattering is proposed.
