By using a propagation scheme for current matrices and an auxiliary mode expansion method, we investigate the transient dynamics of a single molecular junction coupled with a vibrational mode. Our approach is based on the spinless Anderson-Holstein model and the dressed tunnelling approximation for the electronic self-energy in the polaronic regime. The time-dependent currents after a sudden switching on the tunnelling to leads, an abrupt upward step bias pulse and a step potential on the quantum dot are calculated. We show that the strong electron-phonon interaction greatly influences the nonlinear response properties of the system, and gives rise to interesting characteristics on the time traces of transient currents.

We study the impact of the inter-level energy constraints imposed by Haldane Exclusion Statistics on energy relaxation processes in 1-dimensional systems coupled to a bosonic bath. By formulating a second-quantized description of the relevant Fock space, we identify certain universal features of this relaxation dynamics, and show that it is generically slower than that of spinless fermions. Our study focuses on the Calogero-Sutherland model, which realizes Haldane Exclusion statistics exactly in one dimension; however our results apply to any system that has the associated pattern of inter-level occupancy constraints in Fock space.