Trace maps

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12 Scopus citations


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 languageEnglish
Pages (from-to)3525-3542
Number of pages18
JournalInternational Journal of Modern Physics B
Issue number30
StatePublished - 10 Dec 1997

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Condensed Matter Physics


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