Diagrammatic description of a system coupled strongly to a bosonic bath
Michael Marthaler, Juha Leppäkangas · Physical review. B./Physical review. B · 2016
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 a unitary transformation, it can be possible to find a more suitable small expansion parameter. Within such an approach, we construct a formally exact expansion of the master equation on the Keldysh contour. We consider a system diagonally coupled to a bosonic bath and expansion in terms of a nondiagonal hopping term. The lowest-order expansion is equivalent to the so-called $P(E)$ theory or noninteracting blip approximation. The analysis of the higher-order contributions shows that there are two different classes of higher-order diagrams. We study how the convergence of this expansion depends on the form of the spectral function with significant weight at zero frequency.