Abstract
A criterion related to the uncertainty principle is used to determine whether a random walk on a random lattice is localised or extended. Algebraic and exponential localisation lengths are found in one and two dimensions, threshold behaviour in three or more, and mean field behaviour in four or more.
Keywords
Random walkStatistical physicsExponential functionMathematicsRandom fieldLattice (music)Algebraic numberHeterogeneous random walk in one dimensionPhysicsStatisticsMathematical analysis
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Publication Info
- Year
- 1980
- Type
- article
- Volume
- 13
- Issue
- 25
- Pages
- L667-L669
- Citations
- 30
- Access
- Closed
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Cite This
Philip B. Allen
(1980).
Electron localisation in a random potential: a random walk analogue.
Journal of Physics C Solid State Physics
, 13
(25)
, L667-L669.
https://doi.org/10.1088/0022-3719/13/25/001
Identifiers
- DOI
- 10.1088/0022-3719/13/25/001