Resonance Density Research Articles

Statistics of resonances in one-dimensional continuous systems

We study the average density of resonances (DOR) of a disordered one-dimensional continuous open system. The disordered system is semi-infinite, with white-noise random potential, and it is coupled to the external world by a semi-infinite continuous perfect lead. Our main result is an integral representation for the DOR which involves the probability density function of the logarithmic derivative of the wave function at the contact point.

Statistics of resonances in a semi-infinite disordered chain

We study the average density of resonances (DOR) for a semi-infinite disordered chain, coupled to the outside world by a (semi-infinite) perfect lead. A set of equations is derived, which provides the general framework for calculating the average DOR, for an arbitrary disorder and coupling strength. These general equations are applied to the case of weak coupling and an asymptotically exact expression for the averaged DOR is derived, in the limit of small resonance width. This expression is universal, in the sense that it holds for any degree of disorder and everywhere in the (unperturbed) energy band.