Variable-Range Hopping and Quantum Creep in One Dimension

Abstract

We study the quantum nonlinear response to an applied electric field $E$ of a one-dimensional pinned charge-density wave or Luttinger liquid in the 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.