Theory of semiballistic wave propagation

Wave propagation through waveguides, quantum wires, or films with a modest amount of disorder is in the semiballistic 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 modeled by an inhomogeneous density of pointlike 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 Schrödinger 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-Pérot interferometers and double-barrier quantum wells. The predictions are compared with new and existing numerical data and with experiment. The agreement is quite satisfactory. © 1996 The American Physical Society.