Nonlinear I(V) characteristics of Luttinger liquids and gated Hall bars.

Nonlinear current voltage characteristics of a disordered Luttinger liquid are calculated using a perturbative formalism. One finds the nonuniversal power-law characteristics of the form I(V)\ensuremath{\sim}${\mathit{V}}^{1/(2\mathit{g}\mathrm{\ifmmode \tilde{}\else \~{}\fi{}}\mathrm{\ensuremath{-}}1)}$, which is valid both in the superfluid phase when I is small and also in the insulator phase when I is large. Mesoscopic voltage fluctuations are also calculated. One finds Var(\ensuremath{\Delta}V)\ensuremath{\sim}${\mathit{I}}^{4\mathit{g}\mathrm{\ifmmode \tilde{}\else \~{}\fi{}}\mathrm{\ensuremath{-}}3}$. Both the I(V) characteristic and the voltage fluctuations exhibit universal power-law behavior at the superfluid insulator transition where g\ifmmode \tilde{}\else \~{}\fi{}=3/2. The possible application of these results to the nonlinear transport properties of gated Hall bars is discussed.