  We have investigated the dynamics of underdamped Josephson junctions. In
addition to the usual crossover between macroscopic quantum tunnelling and
thermally activated (TA) behaviour we observe in our samples with relatively
small Josephson coupling E_J, for the first time, the transition from TA
behaviour to underdamped phase diffusion. Above the crossover temperature the
threshold for switching into the finite voltage state becomes extremely sharp.
We propose a (T,E_J) phase-diagram with various regimes and show that for a
proper description of it dissipation and level quantization in a metastable
well are crucial.

Mesoscale and Nanoscale Physics;Superconductivity