Weak Anderson localization and enhanced backscatter in reverberation rooms and quantum dots

Enhanced backscatter is studied in closed finite systems which have ballistic internal propagation and diffuse scattering at rough boundaries. Weak localization arguments indicate that the mean-square response at the source should be twice as large as it is at other points. It is argued, however, that the actual ratio is three. Numerical solutions are found to agree with a more detailed theory and to show that the enhanced return factor is two at moderate times, but three at late times comparable to the modal density.