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VOLUME 59 | ISSUE 12 | PAGE 879
The level spacing statistics in a finite 1D disordered sample
The distribution function ./^Δ) of the spacing Δ between nearest energy levels is calculated for a one-dimensional disordered sample with a finite length L. The evaluation proceeds in terms of the Schrodinger equation with a random potential, rather than random matrix ensembles. The common case in which the wavelength of a particle is small compared with the mean free path is considered. Thus Δ is expressed in terms of a solution of the equation with a given energy and all the moments (Δ"1) and then the are calculated with use of a recently developed functional integral method for a ID random potential problem.




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