High-frequency dynamics of wave localization

We study the effect of localization on the propagation of a pulse through a multimode disordered waveguide. The correlator [u(omega(1))u*(omega(2))] O f the transmitted wave amplitude u at two frequencies differing by delta om ega has for large delta omega the stretched exponential tail proportional t o exp(-root tau(D)delta omega/2). The time constant tau(D)=L-2/D is given b y the diffusion coefficient D, even if the length L of the waveguide is muc h greater than the localization length xi. Localization has the effect of m ultiplying the correlator by a frequency-independent factor exp(-L/2 xi), w hich disappears upon breaking time-reversal symmetry. [S1063-651X(99)50412- 1].