Trace maps, invariants, and some of their applications

Details Trace maps, invariants, and some of their applications Trace maps, invariants, and some of their applications

1999-04-26

arxiv.org/abs/math-ph/9904025v1

Int. J. Mod. Phys. B 7 (1993) 1527-1550

Physics

Mathematical Physics

23 pages, including 2 figures, paper made available here due to renewed interest

Scientific paper

10.1142/S021797929300247X

Trace maps of two-letter substitution rules are investigated with special emphasis on the underlying algebraic structure and on the existence of invariants. We illustrate the results with the generalized Fibonacci chains and show that the well-known Fricke character I(x,y,z) = x^2 + y^2 + z^2 - 2 x y z - 1 is not the only type of invariant that can occur. We discuss several physical applications to electronic spectra including the gap-labeling theorem, to kicked two-level systems, and to the classical 1D Ising model with non-commuting transfer matrices.

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