Structure of quantum disordered wave functions: weak localization, far tails, and mesoscopic transport |
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Authors: | BK Nikolić VZ Cerovski |
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Institution: | (1) Department of Physics, Georgetown University, Washington, DC 20057-0995, USA, US;(2) Department of Physics, Virginia Commonwealth University, Richmond, VA 23284, USA, US |
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Abstract: | We report on the comprehensive numerical study of the fluctuation and correlation properties of wave functions in three-dimensional
mesoscopic diffusive conductors. Several large sets of nanoscale samples with finite metallic conductance, modeled by an Anderson
model with different strengths of diagonal box disorder, have been generated in order to investigate both small and large
deviations (as well as the connection between them) of the distribution function of eigenstate amplitudes from the universal
prediction of random matrix theory. We find that small, weak localization-type, deviations contain both diffusive contributions
(determined by the bulk and boundary conditions dependent terms) and ballistic ones which are generated by electron dynamics
below the length scale set by the mean free path ℓ. By relating the extracted parameters of the functional form of nonperturbative
deviations (“far tails”) to the exactly calculated transport properties of mesoscopic conductors, we compare our findings
based on the full solution of the Schr?dinger equation to different approximative analytical treatments. We find that statistics
in the far tail can be explained by the exp-log-cube asymptotics (convincingly refuting the log-normal alternative), but with
parameters whose dependence on ℓ is linear and, therefore, expected to be dominated by ballistic effects. It is demonstrated
that both small deviations and far tails depend explicitly on the sample size--the remaining puzzle then is the evolution
of the far tail parameters with the size of the conductor since short-scale physics is supposedly insensitive to the sample
boundaries.
Received 19 August 2002
Published online 19 November 2002 |
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Keywords: | PACS 73 21 -b Electron states and collective excitations in multilayers quantum wells mesoscopic and nanoscale systems – 73 20 Fz Weak or Anderson localization – 73 23 -b Electronic transport in mesoscopic systems – 05 45 Mt Quantum chaos semiclassical methods |
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