Asymptotic forms for the states of weakly disordered systems
- 1 June 1986
- journal article
- research article
- Published by Taylor & Francis in Philosophical Magazine Part B
- Vol. 53 (6) , 545-559
- https://doi.org/10.1080/13642818608240667
Abstract
The Schrödinger equation is solved asymptotically in separation for a two-dimensional and a three-dimensional system, each with weak disorder similar to the Anderson model. Distributions of the phase and logarithm of the amplitude of the wavefunctions are found to be Gaussian with means and widths which in two dimensions describe power-law localized states and exponentially localized states separated in energy by a mobility edge, and in three dimensions describe extended states and exponentially localized states also separated in energy by a mobility edge. The results do not obey a single-parameter scaling law.Keywords
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