The spectrum of a discrete Schrödinger operator with a hierarchically distributed potential is studied both by a renormalization group technique and by numerical analysis. A suitable choice of the potential makes it possible to reduce the original problem to a two-dimensional map. Scaling laws for the band-edge energyE be and for the integrated density of states eegr are predicted together with the global properties of the spectrum. Different scaling regimes are obtained depending on a hierarchy positive parameterR: for R<1 the="" usual="" scaling="" laws="" for="" the="" periodic="" case="" are="" obtained,="" while="">R>1/2 the scaling behavior depends explicitly onR.

The spectrum of a one-dimensional hierarchical model / Livi, R.; Maritan, A.; Ruffo, S.. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - 52:3-4(1988), pp. 595-608. [10.1007/BF01019719]

The spectrum of a one-dimensional hierarchical model

Ruffo, S.
1988-01-01

Abstract

The spectrum of a discrete Schrödinger operator with a hierarchically distributed potential is studied both by a renormalization group technique and by numerical analysis. A suitable choice of the potential makes it possible to reduce the original problem to a two-dimensional map. Scaling laws for the band-edge energyE be and for the integrated density of states eegr are predicted together with the global properties of the spectrum. Different scaling regimes are obtained depending on a hierarchy positive parameterR: for R<1 the="" usual="" scaling="" laws="" for="" the="" periodic="" case="" are="" obtained,="" while="">R>1/2 the scaling behavior depends explicitly onR.
1988
52
3-4
595
608
Livi, R.; Maritan, A.; Ruffo, S.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/14370
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