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Trace Maps

Published:1997-12-10 Issue:30 Volume:11 Page:3525-3542
ISSN:0217-9792
Container-title:International Journal of Modern Physics B
language:en
Short-container-title:Int. J. Mod. Phys. B

Author:

Avishai Yshai¹,Berend Daniel²,Tkachenko Vadim²

Affiliation:

1. Department of Physics, Ben-Gurion University, Beer-Sheva 84105, Israel

2. Department of Mathematics and Computer Science, Ben-Gurion University, Beer-Sheva 84105, Israel

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Condensed Matter Physics,Statistical and Nonlinear Physics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0217979297001763

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