  We construct model master equations for local quantum dissipation. The master
equations are in the form of Lindblad generators, with imposed constraints that
the dissipations be strictly linear (i.e. ohmic), isotropic and translationally
invariant. A particular form for is chosen to satisfy the constraints. The
resulting master equations are given in both the Schr\"odinger and Heisenberg
forms. We obtain fluctuation-dissipation relations, and discuss the relaxation
of average kinetic energy to effective thermal equilibrium values. We compare
our results to the Dekker and the Caldeira-Leggett master equations. These
master equations allow a more general approach to quantum dissipation and the
dynamics of quantum coherence to account for the nontrivial system-environment
coupling in a local environment.
