  We study the quantum non linear response to an applied electric field $E$ of
a one dimensional pinned charge density wave or Luttinger liquid in presence of
disorder. From an explicit construction of low lying metastable states and of
bounce instanton solutions between them, we demonstrate quantum creep $v = e^{-
c/E^{1/2}}$ as well as a sharp crossover at $E=E^*$ towards a linear response
form consistent with variable range hopping arguments, but dependent only on
electronic degrees of freedom.
