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Numerical studies of localization in disordered systems
Abstract
The results of numerical work on the Anderson model of disordered systems are presented. The sensitivity of the eigenvalues to the choice of periodic or antiperiodic boundary conditions is used as a criterion for localization, and the theory of this criterion is discussed. For the two dimensional square lattice this criterion gives a reasonably sharp result for the onset of localization which is not in conflict with other criteria of localization, and it is found that localization occurs far more easily than Anderson's theory suggests. For the diamond lattice the onset of localization is less sharply defined, and localization occurs less easily than for the square lattice, but more easily than in Anderson's theory.
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Citations
Cites
Absence of Diffusion in Certain Random Lattices
Anderson, P. W. (1958) · Physical Review · doi:10.1103/physrev.109.1492 · Cited by 12,468
Cited by
Electronic properties of two-dimensional systems
Ando, T., Fowler, A. B., & Stern, F. (1982) · Reviews of Modern Physics · doi:10.1103/revmodphys.54.437 · Cited by 7,455
Scaling Theory of Localization: Absence of Quantum Diffusion in Two Dimensions
Abrahams, E., Anderson, P. W., Licciardello, D. C., & Ramakrishnan, T. V. (1979) · Physical Review Letters · doi:10.1103/physrevlett.42.673 · Cited by 6,134
Random-matrix theory of quantum transport
Beenakker, C. W. J. (1997) · Reviews of Modern Physics · doi:10.1103/revmodphys.69.731 · Cited by 2,551
Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
Lewenstein, M., Sanpera, A., Ahufinger, V., Damski, B., Sen(De), A., & Sen, U. (2007) · Advances in Physics · doi:10.1080/00018730701223200 · Cited by 2,104
Localization: theory and experiment
Kramer, B., & MacKinnon, A. (1993) · Reports on Progress in Physics · doi:10.1088/0034-4885/56/12/001 · Cited by 1,926
Metadata
- Authors
- Edwards, J. T., & Thouless, D. J.
- Venue
- Journal of Physics C: Solid State Physics
- Publisher
- IOP Publishing
- Published
- 1972-04-27
- Volume
- 5
- Issue
- 8
- Pages
- 807-820
- ISSN
- 0022-3719 (ISSN-L)
- OpenAlex
- W2048710809
- Cited by
- 622
- References
- 1
- FWCI
- 9.92
- Type
- journal article
- Language
- en
- Open access
- closed
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- Edwards, J. T., & Thouless, D. J. (1972). Numerical studies of localization in disordered systems. Journal of Physics C: Solid State Physics. https://doi.org/10.1088/0022-3719/5/8/007
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
