  We study theoretically two effects related to impurity depinning that are
common for 1D Luttinger liquid (LL) and linear-chain CDW conductors. First, we
consider the electron transport through a single impurity in a 1D conducting
channel and study a new regime of conduction related to LL sliding at voltage
above a threshold one. The DC current in this regime is accompanied by
oscillations with frequency $f =I/e$. This resembles the CDW depinning in
linear-chain conductors, the Josephson effect, and the Coulomb blockade.
Second, we found that strong pinning of the LL by impurities leads to a
magnetic field dependence of the low-temperature specific heat similar to that
observed experimentally in CDW compounds. We interpret this in favor of
possibility of formation of the LL in linear-chain compounds.
