  We have recently calculated exact non-equilibrium quantum transport
properties through a point contact in a Luttinger liquid. Using a particular
quasiparticle basis of the Hilbert space dictated by integrability, we here
compute explicitly the exact $I(V)$ characteristic and conductance out of
equilibrium as a function of driving voltage $V$ and temperature $T$. These are
described by universal scaling functions of two variables, the scaled
point-contact interaction strength, and $V/T$. The differential-conductance
curve as a function of the interaction strength broadens significantly as $V/T$
is increased, and develops a pronounced maximum at a (universal) critical value
$(e V/k_B T)=7.18868...$. In addition, we derive an exact duality between
strong and weak backscattering. The theory presented here has recently been
realized experimentally in resonant tunneling-transport experiments between
edge states in fractional quantum Hall effect devices. In this context the
exact duality is between electron tunneling and Laughlin-quasiparticle
tunneling.
