  Superbursts are rare day-long Type I X-ray bursts due to carbon flashes on
accreting neutron stars in low-mass X-ray binaries. They heat the neutron star
envelope such that the burning of accreted hydrogen and helium becomes stable,
and the common shorter X-ray bursts are quenched. Short bursts reappear only
after the envelope cools down. We study multi-zone one-dimensional models of
the neutron star envelope, in which we follow carbon burning during the
superburst, and we include hydrogen and helium burning in the atmosphere above.
We investigate both the case of a solar composition and a helium-rich
atmosphere. This allows us to study for the first time a wide variety of
thermonuclear burning behavior as well as the transitions between the different
regimes in a self-consistent manner. For solar composition, burst quenching
ends much sooner than previously expected. This is because of the complex
interplay between the 3-alpha, hot CNO, and CNO breakout reactions. Stable
burning of hydrogen and helium transitions via marginally stable burning (mHz
QPOs) to less energetic bursts with short recurrence times. We find a
short-lived bursting mode where weaker and stronger bursts alternate.
Eventually the bursting behavior changes back to that of the pre-superburst
bursts. Because of the scarcity of observations, this transition has not been
directly detected after a superburst. Using the MINBAR burst catalog we
identify the shortest upper limit on the quenching time for 4U 1636-536, and
derive further constraints on the time scale on which bursts return.
