  The dissipation induced by a metallic gate on the low-energy properties of
interacting 1D electron liquids is studied. As function of the distance to the
gate, or the electron density in the wire, the system undergoes a quantum phase
transition from the Tomonaga-Luttinger liquid state to two kinds of dissipative
phases, one of them with a finite spatial correlation length. We also define a
dual model, which describes an attractive one dimensional metal with a
Josephson coupling to a dirty metallic lead.
