  Excess emission, associated with warm, dust belts, commonly known as
exozodis, has been observed around a third of nearby stars. The high levels of
dust required to explain the observations are not generally consistent with
steady-state evolution. A common suggestion is that the dust results from the
aftermath of a dynamical instability, an event akin to the Solar System's Late
Heavy Bombardment. In this work, we use a database of N-body simulations to
investigate the aftermath of dynamical instabilities between giant planets in
systems with outer planetesimal belts. We find that, whilst there is a
significant increase in the mass of material scattered into the inner regions
of the planetary system following an instability, this is a short-lived effect.
Using the maximum lifetime of this material, we determine that even if every
star has a planetary system that goes unstable, there is a very low probability
that we observe more than a maximum of 1% of sun-like stars in the aftermath of
an instability, and that the fraction of planetary systems currently in the
aftermath of an instability is more likely to be limited to <0.06. This
probability increases marginally for younger or higher mass stars. We conclude
that the production of warm dust in the aftermath of dynamical instabilities is
too short-lived to be the dominant source of the abundantly observed
exozodiacal dust.
