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We have recently calculated exact non-equilibrium quantum transportproperties through a point contact in a Luttinger liquid. Using a particularquasiparticle basis of the Hilbert space dictated by integrability, we herecompute explicitly the exact $I(V)$ characteristic and conductance out ofequilibrium as a function of driving voltage $V$ and temperature $T$. These aredescribed by universal scaling functions of two variables, the scaledpoint-contact interaction strength, and $V/T$. The differential-conductancecurve 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 betweenstrong and weak backscattering. The theory presented here has recently beenrealized experimentally in resonant tunneling-transport experiments betweenedge states in fractional quantum Hall effect devices. In this context theexact duality is between electron tunneling and Laughlin-quasiparticletunneling.Comment: 38 pages (22 in little format); uses harvmac macros. Two uuencoded  figures are appended. Revised version corrects many typo

Exact nonequilibrium transport through point contacts in quantum wires and fractional quantum Hall devices