  We study a generic problem of dissipative quantum mechanics, a small local
quantum system with discrete states coupled in an arbitrary way (i.e. not
necessarily linear) to several infinitely large particle or heat reservoirs.
For both bosonic or fermionic reservoirs we develop a quantum field-theoretical
diagrammatic formulation in Liouville space by expanding systematically in the
reservoir-system coupling and integrating out the reservoir degrees of freedom.
As a result we obtain a kinetic equation for the reduced density matrix of the
quantum system. Based on this formalism, we present a formally exact
perturbative renormalization group (RG) method from which the kernel of this
kinetic equation can be calculated. It is demonstrated how the nonequilibrium
stationary state (induced by several reservoirs kept at different chemical
potentials or temperatures), arbitrary observables such as the transport
current, and the time evolution into the stationary state can be calculated.
Most importantly, we show how RG equations for the relaxation and dephasing
rates can be derived and how they cut off generically the RG flow of the
vertices. The method is based on a previously derived real-time RG technique
but formulated here in Laplace space and generalized to arbitrary
reservoir-system couplings. Furthermore, for fermionic reservoirs with flat
density of states, we make use of a recently introduced cutoff scheme on the
imaginary frequency axis which has several technical advantages. We demonstrate
the method by applying it to the nonequilibrium isotropic Kondo model in
1-loop. We present a systematic way to solve the RG equations analytically in
the weak-coupling limit and provide an outlook of the applicability to the
strong-coupling case.
