Non-Golden-Rule behaviour of phonon-assisted quantum transport

Abstract

In a Kubo response approach the occupational decay is characterised by an oscillatory transport coefficient omega ₀ and a damping constant Gamma ₀. It is shown that the Fulton-Gouterman transformation has a fundamental bearing on quantum transport and allows for exact statements about the transport quantities omega ₀ and Gamma ₀. It is proven that in the limit of a small transitive parameter Delta both omega ₀ and Gamma ₀ depend linearly on Delta . It is further shown that the temperature behaviour of omega ₀ and Gamma ₀ is different in the one-, few- and many-mode (N>>1) cases. In the latter case the dependence on Delta ² of Gamma ₀ takes over, but even here the result cannot be identified with a Golden-Rule result. Finally, the exact temperature law of omega ₀²+ Gamma ₀² is given up to order Delta ² in the one-mode case.