Statistics of resonances in one-dimensional continuous systems

JOSHUA FEINBERG

Physics Department, University of Haifa at Oranim, Tivon 36006, Israel

and

Physics Department, Technion, Haifa 32000, Israel

E-mail: joshua@physics.technion.ac.il

Abstract. 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.

Keywords. Resonances; spectral determinant; disordered systems;

Fokker--Planck equation; average density of resonances.

PACS Nos 03.65.Yz; 03.65.Nk; 72.15.Rn