  The temporal evolution of microwave pulses transmitted through random
dielectric samples is obtained from the Fourier transform of field spectra.
Large fluctuations are found in the local or single channel delay time, which
is the first temporal moment of the transmitted pulse at a point in the output
speckle pattern. Both positive and negative values of local delay time are
observed. The widest distribution is found at low intensity values near a phase
singularity in the transmitted speckle pattern. In the limit of long duration,
narrow-bandwidth incident pulses, the single channel delay time equals the
spectral derivative of the phase of the transmitted field. Fluctuations of the
phase of the transmitted field thus reflect the underlying statistics of
dynamics in mesoscopic systems.
