Scaling studies of the resistance of the one-dimensional Anderson model with general disorder
- 15 November 1981
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 24 (10), 5583-5596
- https://doi.org/10.1103/physrevb.24.5583
Abstract
The resistance of a one-dimensional Anderson model with both diagonal and off-diagonal disorder is studied by analytic and numerical techniques. A recursive method is developed and used to derive an exact scaling law for the average resistance at for arbitrary disorder, and for in the limit of weak disorder. The average resistance grows exponentially with , the length of the sample, in all cases. The typical resistance is also found to grow exponentially with in all cases, except for purely off-diagonal disorder at , where . An explanation is given for the existence of this special case and it is shown that all our results are consistent with a lognormal probability distribution of the resistance for . Quantitative estimates are made of the reliability of numerically performed averages which show that a numerical average will converge only very slowly to the analytic result. This provides a qualitative explanation of the slower than linear growth of with found in several numerical calculations; its consequences for experiment are also explored.
Keywords
This publication has 21 references indexed in Scilit:
- Off-diagonal disorder in one-dimensional systemsPhysical Review B, 1981
- Derivation of the Landauer conductance formulaPhysical Review B, 1981
- Probability distribution and new scaling law for the resistance of a one-dimensional Anderson modelPhysical Review B, 1981
- Transmission of particles through a random one-dimensional potentialPhysical Review B, 1981
- Static Conductance and Scaling Theory of Localization in One DimensionPhysical Review Letters, 1981
- New method for a scaling theory of localizationPhysical Review B, 1980
- Numerical studies of inverse localisation length in one dimensionJournal of Physics C: Solid State Physics, 1980
- Resistance fluctuations in disordered one-dimensional conductorsJournal of Physics C: Solid State Physics, 1980
- A central limit theorem for the disordered harmonic chainCommunications in Mathematical Physics, 1975
- Electrical resistance of disordered one-dimensional latticesPhilosophical Magazine, 1970