Wave propagation through waveguides, quantum wires or films with a modest
amount of disorder is in the semi-ballistic regime when in the transversal
direction(s) almost no scattering occurs, while in the long direction(s) there
is so much scattering that the transport is diffusive. For such systems
randomness is modelled by an inhomogeneous density of point-like scatterers.
These are first considered in the second order Born approximation and then
beyond that approximation. In the latter case it is found that attractive point
scatterers in a cavity always have geometric resonances, even for Schr\"odinger
wave scattering. In the long sample limit the transport equation is solved
analytically. Various geometries are considered: waveguides, films, and
tunneling geometries such as Fabry-P\'erot interferometers and double barrier
quantum wells. The predictions are compared with new and existing numerical
data and with experiment. The agreement is quite satisfactory.Comment: 24 pages Revtex; 10 figure