  We have investigated the weakly non-linear quantum transport properties of a
two-dimensional quantum conductor. We have developed a numerical scheme which
is very general for this purpose. The nonlinear conductance is computed by
explicitly evaluating the various partial density of states, the sensitivity
and the characteristic potential. Interesting spatial structure of these
quantities are revealed. We present detailed results concerning the crossover
behavior of the second order nonlinear conductance when the conductor changes
from geometrically symmetrical to asymmetrical. Other issues of interests such
as the gauge invariance are also discussed.
