Trace maps

Yshai Avishai; Daniel Berend; Vadim Tkachenko

doi:10.1142/S0217979297001763

Trace maps

Yshai Avishai, Daniel Berend, Vadim Tkachenko

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12 Scopus citations

Abstract

Trace maps for products of transfer matrices prove to be an important tool in the investigation of electronic spectra and wave functions of one-dimensional quasiperiodic systems. These systems belong to a general class of substitution sequences. In this work we review the various stages of development in constructing trace maps for products of (2 × 2) matrices generated by arbitrary substitution sequences. The dimension of the underlying space of the trace map obtained by means of this construction is the minimal possible, namely 3r - 3 for an alphabet of size r ≥ 2. In conclusion, we describe some results from the spectral theory of discrete Schrödinger operators with substitution potentials.

Original language	English
Pages (from-to)	3525-3542
Number of pages	18
Journal	International Journal of Modern Physics B
Volume	11
Issue number	30
DOIs	https://doi.org/10.1142/S0217979297001763
State	Published - 10 Dec 1997

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Condensed Matter Physics

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AU - Tkachenko, Vadim

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AB - Trace maps for products of transfer matrices prove to be an important tool in the investigation of electronic spectra and wave functions of one-dimensional quasiperiodic systems. These systems belong to a general class of substitution sequences. In this work we review the various stages of development in constructing trace maps for products of (2 × 2) matrices generated by arbitrary substitution sequences. The dimension of the underlying space of the trace map obtained by means of this construction is the minimal possible, namely 3r - 3 for an alphabet of size r ≥ 2. In conclusion, we describe some results from the spectral theory of discrete Schrödinger operators with substitution potentials.

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Trace maps

Abstract

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