We study the problem of Luttinger liquids interacting with an active
environment. We are particularly interested in how dissipation affects the
response and correlation functions of non-isolated Luttinger liquids. We show
that the exchange of particles, energy, and momentum lead to changes in the
exponents characterizing the various correlations functions. We discuss the
importance of the zero mode physics in this context.Comment: Revtex, 4 pages. Final version published in PR