Delay-time and thermopower distributions at the spectrum edges of a chaotic scatterer

We study chaotic scattering outside the wideband limit, as the Fermi energy E_F approaches the band edges E_B of a one-dimensional lattice embedding a scattering region of M sites. We show that the delay-time and thermopower distributions differ near the edges from the universal expressions valid in the bulk. To obtain the asymptotic universal forms of these edge distributions, one must keep constant the energy distance E _F-E_B measured in units of the same energy scale proportional to M^-1^/3 which is used for rescaling the energy level spacings at the spectrum edges of large Gaussian matrices. In particular the delay time and the thermopower have the same universal edge distributions for arbitrary M as those for an M=2 scatterer, which we obtain analytically.