  We study the ensemble-averaged conductance as a function of applied magnetic
field for ballistic electron transport across few-channel microstructures
constructed in the shape of classically chaotic billiards. We analyse the
results of recent experiments, which show suppression of weak localization due
to magnetic field, in the framework of random-matrix theory. By analysing a
random-matrix Hamiltonian for the billiard-lead system with the aid of
Landauer's formula and Efetov's supersymmetry technique, we derive a universal
expression for the weak-localization contribution to the mean conductance that
depends only on the number of channels and the magnetic flux. We consequently
gain a theoretical understanding of the continuous crossover from orthogonal
symmetry to unitary symmetry arising from the violation of time-reversal
invariance for generic chaotic systems.
