  This work makes progress on the issue of global- vs. local- master equations.
Global master equations like the Redfield master equation (following from
standard Born- and Markov- approximation) require a full diagonalization of the
system Hamiltonian. This is especially challenging for interacting quantum
many-body systems. We discuss a short-bath-correlation-time expansion in
reciprocal (energy) space, leading to a series expansion of the jump operator,
which avoids a diagonalization of the Hamiltonian. For a bath that is coupled
locally to one site, this typically leads to an expansion of the global
Redfield jump operator in terms of local operators. We additionally map the
local Redfield master equation to an approximate Lindblad form, giving an
equation which has the same conceptual advantages of traditional local Lindblad
approaches, while being applicable in a much broader class of systems. Our
ideas give rise to a non-heuristic foundation of local master equations, which
can be combined with established many-body methods.
