  The classical sine-Gordon model permits integrable discontinuities, or
jump-defects, where the conditions relating the fields on either side of a
defect are Backlund transformations frozen at the defect location. The purpose
of this article is to explore the extent to which this idea may be extended to
the quantum sine-Gordon model and how the striking features of the classical
model may translate to the quantum version. Assuming a positive defect
parameter there are two types of defect. One type, carrying even charge, is
stable, but the other type, carrying odd charge, is unstable and may be
considered as a resonant bound state of a soliton and a stable defect. The
scattering of solitons with defects is considered in detail, as is the
scattering of breathers, and in all cases the jump-defect is purely
transmitting. One surprising discovery concerns the lightest breather. Its
transmission factor is independent of the bulk coupling - a property
susceptible to a perturbative check, but not shared with any of the other
breathers. It is argued that classical jump-defects can move and some comments
are made concerning their quantum scattering matrix.
