Microscopic versus mesoscopic local density of states in one-dimensional localization

Details Microscopic versus mesoscopic local density of states in one-dimensional localization Microscopic versus mesoscopic local density of states in one-dimensional localization

2001-07-18

arxiv.org/abs/cond-mat/0107383v1

Phys. Rev. B 65, 121101(R) (2002)

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 2 figures

Scientific paper

10.1103/PhysRevB.65.121101

We calculate the probability distribution of the local density of states $\nu$ in a disordered one-dimensional conductor or single-mode waveguide, attached at one end to an electron or photon reservoir. We show that this distribution does not display a log-normal tail for small $\nu$, but diverges instead $\propto\nu^{-1/2}$. The log-normal tail appears if $\nu$ is averaged over rapid oscillations on the scale of the wavelength. There is no such qualitative distinction between microscopic and mesoscopic densities of states if the levels are broadened by inelastic scattering or absorption, rather than by coupling to a reservoir.

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