Distribution of the delay time and the dwell time for wave reflection from a long random potential

We re-examine and correct an earlier derivation of the distribution of the Wigner phase delay time for wave reflection from a long one-dimensional disordered conductor treated in the continuum limit. We then numerically compare the distributions of the Wigner phase delay time and the dwell time, the latter being obtained by the use of an infinitesimal imaginary potential as a clock, and investigate the effects of strong disorder and a periodic (discrete) lattice background. We find that the two distributions coincide even for strong disorder, but only for energies well away from the band-edges.Comment: Final version with minor corrections in text, 4 pages, 2 PS figure

Propagating and evanescent waves in absorbing media

We compare the behavior of propagating and evanescent light waves in absorbing media with that of electrons in the presence of inelastic scattering. The imaginary part of the dielectric constant results primarily in an exponential decay of a propagating wave, but a phase shift for an evanescent wave. We then describe how the scattering of quantum particles out of a particular coherent channel can be modeled by introducing an imaginary part to the potential in analogy with the optical case. The imaginary part of the potential causes additional scattering which can dominate and actually prevent absorption of the wave for large enough values of the imaginary part. We also discuss the problem of maximizing the absorption of a wave and point out that the existence of a bound state greatly aids absorption. We illustrate this point by considering the absorption of light at the surface of a metal.Comment: Brief Review, to appear in the American Journal of Physics, http://www.kzoo.edu/ajp