We present a simple approach to Anderson localization in one-dimensional disordered lattices. We introduce the tight-binding model in which one orbital and a single random energy are assigned to each lattice site, and the hopping integrals are constant and restricted to nearest-neighbor sites. The localization of eigenstates is explained by two-parameter scaling arguments. We compare the size scaling of the level spacing in the bare energy spectrum of the quasi-particle (in the ideal lattice) with the size scaling of the renormalized disorder seen by the quasi-particle. The former decreases faster than the latter with increasing system size, giving rise to mixing and to the localization of the bare quasi-particle wave functions in the thermodynamic limit. We also provide a self-consistent calculation of the localization length and show how this length can be obtained from optical absorption spectra for Frenkel excitons.
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February 2004
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February 01 2004
A simple approach to Anderson localization in one-dimensional disordered lattices
F. Domı́nguez-Adame;
F. Domı́nguez-Adame
GISC, Departamento de Fı́sica de Materiales, Universidad Complutense, E-28040 Madrid, Spain
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V. A. Malyshev
V. A. Malyshev
GISC, Departamento de Fı́sica de Materiales, Universidad Complutense, E-28040 Madrid, Spain
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Am. J. Phys. 72, 226–230 (2004)
Article history
Received:
February 13 2003
Accepted:
June 02 2003
Citation
F. Domı́nguez-Adame, V. A. Malyshev; A simple approach to Anderson localization in one-dimensional disordered lattices. Am. J. Phys. 1 February 2004; 72 (2): 226–230. https://doi.org/10.1119/1.1593660
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