In this PhD thesis, we investigate the non-equilibrium behaviour of Josephson junctions using microscopically-exact approaches. Transcending the existing theories, which are either limited to the steady-state regime with a DC voltage bias, or based on perturbative expansions in the Josephson coupling, we reveal several interesting features arising from the interplay of the various fundamental physical phenomena underlying the Josephson effect. In the transient regime of tunnel junctions, we show that beyond the conventional () current, sharp voltage pulses lead to a modified current-phase relation resembling ( (t) /2), driven by the interference of sub-gap quasiparticles. Returning back to the steady-state regime, we find that in addition to the superconducting phase difference, the Josephson current can also provide a window into the dynamics of the superconducting gap---the Higgs mode. This results in an enhanced second harmonic current, (2 (t) ). Additionally, we find that this results in modified Shapiro steps under microwave radiation. Finally, we develop a microscopic theory for DC current-biased junctions, bridging gaps in existing models and recovering the experimentally observed features in the current-voltage characteristics.
Aritra Lahiri (Thu,) studied this question.