  We show how one can obtain a lower bound for the electrical, spin or heat
conductivity of correlated quantum systems described by Hamiltonians of the
form H = H0 + g H1. Here H0 is an interacting Hamiltonian characterized by
conservation laws which lead to an infinite conductivity for g=0. The small
perturbation g H1, however, renders the conductivity finite at finite
temperatures. For example, H0 could be a continuum field theory, where momentum
is conserved, or an integrable one-dimensional model while H1 might describe
the effects of weak disorder. In the limit g to 0, we derive lower bounds for
the relevant conductivities and show how they can be improved systematically
using the memory matrix formalism. Furthermore, we discuss various applications
and investigate under what conditions our lower bound may become exact.
