The level spacing statistics in a finite 1D disordered sample

Kolokolov I.V.

The distribution function *V *(Δ) of the spacing Δ between nearest enegry levels is calculated for one-dimensional disordered sample with a finite length *L. *The evaluation proceeds in terms of the Schroedinger equation with a random potential rather than random matrix ensembles. I consider the common case when a particle's wavelength is small comparing with the mean free path. Thus Δ is expressed in terms of a solution of the equation with a given energy and all the moments < Δ™ > and then 'Ρ(Δ) are calculated with the use of recently developed functional integral method for ID random potential problem.