A remark on the trace-map for the Silver mean sequence

TL;DR

This paper investigates the Silver mean sequence using a transfer-matrix approach, deriving a recurrence relation for transfer-matrix traces and identifying an invariant of the trace-map to understand its electronic properties.

Contribution

It introduces a new recurrence relation for transfer-matrix traces and discovers an invariant of the trace-map specific to the Silver mean sequence.

Findings

Derived a recurrence relation for transfer-matrix traces

Identified an invariant of the trace-map

Characterized electronic properties of the quasicrystal

Abstract

In this work we study the Silver mean sequence based on substitution rules by means of a transfer-matrix approach. Using transfer-matrix method we find a recurrence relation for the traces of general transfer-matrices which characterizes electronic properties of the quasicrystal in question. We also find an invariant of the trace-map.