Diagrammatic description of a quantum system coupled to strong noise

Michael Marthaler, Juha Leppäkangas

Published 2015-10-07Version 1

We study a system-bath description in the strong coupling regime, where it is not possible to derive a master equation for the reduced density matrix by a direct expansion in the system-bath coupling. A particular example is a bath with significant spectral weight at low frequencies. Through an unitary transformation it can be possible to find a more suitable small expansion parameter. Within this approach we construct a formally exact expansion of the master equation on the Keldysh contour. The lowest-order expansion is similar to the so-called $P(E)$-theory or non-interacting blip approximation (NIBA). The analysis of the higher-order contributions shows that there are two different classes of higher-order diagrams. We study how the form of the spectral function affects their convergence.