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The propagation of classical wave in disordered media at the Andersonlocalization transition is studied. Our results show that the classical wavesmay follow a different scaling behavior from that for electrons. For electrons,the effect of weak localization due to interference of recurrent scatteringpaths is limited within a spherical volume because of electron-electron orelectron-phonon scattering, while for classical waves, it is the samplegeometry that determine the amount of recurrent scattering paths thatcontribute. It is found that the weak localization effect is weaker in bothcubic and slab geometry than in spherical geometry. As a result, the averagedstatic diffusion constant D(L) scales like ln(L)/L in cubic or slab geometryand the corresponding transmission follows <T(L)>~ln L/L^2. This is in contrastto the behavior of D(L)~1/L and <T(L)>~1/L^2 obtained previously for electronsor spherical samples. For wave dynamics, we solve the Bethe-Salpeter equationin a disordered slab with the recurrent scattering incorporated in aself-consistent manner. All of the static and dynamic transport quantitiesstudied are found to follow the scaling behavior of D(L). We have alsoconsidered position-dependent weak localization effects by using a plausibleform of position-dependent diffusion constant D(z). The same scaling behavioris found, i.e., <T(L)>~ln L/L^2.Comment: 11 pages, 12 figures. Submitted to Phys. Rev. B on 3 May 200

Scaling behavior of classical wave transport in mesoscopic media at the localization transition