  The variable range hopping results for noninteracting electrons of Mott and
Shklovskii are generalized to 1D disordered charge density waves and Luttinger
liquids using an instanton approach. Following a recent paper by Nattermann,
Giamarchi and Le Doussal [Phys. Rev. Lett. {\bf 91}, 56603 (2003)] we calculate
the quantum creep of charges at zero temperature and the linear conductivity at
finite temperatures for these systems. The hopping conductivity for the short
range interacting electrons acquires the same form as for noninteracting
particles if the one-particle density of states is replaced by the
compressibility. In the present paper we extend the calculation to dissipative
systems and give a discussion of the physics after the particles materialize
behind the tunneling barrier. It turns out that dissipation is crucial for
tunneling to happen. Contrary to pure systems the new metastable state does not
propagate through the system but is restricted to a region of the size of the
tunneling region. This corresponds to the hopping of an integer number of
charges over a finite distance. A global current results only if tunneling
events fill the whole sample. We argue that rare events of extra low tunneling
probability are not relevant for realistic systems of finite length. Finally we
show that an additional Coulomb interaction only leads to small logarithmic
corrections.
