Trace and antitrace maps for aperiodic sequences, their extensions and applications

Details Trace and antitrace maps for aperiodic sequences, their extensions and applications Trace and antitrace maps for aperiodic sequences, their extensions and applications

2000-05-26

arxiv.org/abs/cond-mat/0005463v2

Phys. Rev. B 62 (2000) 14020-14031

Physics

Condensed Matter

Disordered Systems and Neural Networks

13 pages, REVTeX, now also includes applications to electronic systems, some references added

Scientific paper

10.1103/PhysRevB.62.14020

We study aperiodic systems based on substitution rules by means of a transfer-matrix approach. In addition to the well-known trace map, we investigate the so-called `antitrace' map, which is the corresponding map for the difference of the off-diagonal elements of the 2x2 transfer matrix. The antitrace maps are obtained for various binary, ternary and quaternary aperiodic sequences, such as the Fibonacci, Thue-Morse, period-doubling, Rudin-Shapiro sequences, and certain generalizations. For arbitrary substitution rules, we show that not only trace maps, but also antitrace maps exist. The dimension of the our antitrace map is r(r+1)/2, where r denotes the number of basic letters in the aperiodic sequence. Analogous maps for specific matrix elements of the transfer matrix can also be constructed, but the maps for the off-diagonal elements and for the difference of the diagonal elements coincide with the antitrace map. Thus, from the trace and antitrace map, we can determine any physical quantity related to the global transfer matrix of the system. As examples, we employ these dynamical maps to compute the transmission coefficients for optical multilayers, harmonic chains, and electronic systems.

Affiliated with

Also associated with

No associations

Rating

Trace and antitrace maps for aperiodic sequences, their extensions and applications does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Trace and antitrace maps for aperiodic sequences, their extensions and applications, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Trace and antitrace maps for aperiodic sequences, their extensions and applications will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-706892