We study the time-evolving currents flowing in an interacting ring-shaped nanostructure after a bias voltage has been switched on. The source-to-drain current exhibits the expected relaxation towards its quasistatic equilibrium value at a rate 0 reflecting the lead-induced broadening of the ring states. In contrast, the current circulating within the ring decays with a different rate , which is a rapidly decaying function of the interaction strength and thus can take values orders of magnitude below 0 . This implies the existence of a regime in which the nanostructure is far from equilibrium even though the transmitted current is already stationary. We discuss experimental setups to observe the long-lived ring transients.

We numerically calculate the local density of states (LDOS) of a one-dimensional Mott insulator with open boundaries, which is modelled microscopically by a (extended) Hubbard chain at half filling. In the Fourier transform of the LDOS we identify several dispersing features corresponding to propagating charge and spin degrees of freedom, thus providing a visualisation of the spin-charge separation in the system. We also consider the effect of an additional boundary potential, which, if sufficiently strong, leads to the formation of a boundary bound state which is clearly visible in the LDOS as a non-dispersing feature inside the Mott gap.

We study the time evolution of the two-point correlation functions in the XXZ Heisenberg chain after a finite-time quantum quench in the anisotropy. We compare results from numerical simulations to ones obtained in the Luttinger model and find good agreement. We analyse the spreading of the correlations and the associated light-cone features. We observe a delay in the appearance of the light cone as compared to the sudden-quench setup, and link this delay to the properties of the quench protocol.

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