  Finite strips, composed of a periodic stacking of infinite quasiperiodic
Fibonacci chains, have been investigated in terms of their electronic
properties. The system is described by a tight binding Hamiltonian. The
eigenvalue spectrum of such a multi-strand quasiperiodic network is found to be
sensitive on the mutual values of the intra-strand and inter-strand tunnel
hoppings, whose distribution displays a unique three-subband self-similar
pattern in a parameter subspace. In addition, it is observed that special
numerical correlations between the nearest and the next-nearest neighbor
hopping integrals can render a substantial part of the energy spectrum
absolutely continuous. Extended, Bloch like functions populate the above
continuous zones, signalling a complete delocalization of single particle
states even in such a non-translationally invariant system, and more
importantly, a phenomenon that can be engineered by tuning the relative
strengths of the hopping parameters. A commutation relation between the
potential and the hopping matrices enables us to work out the precise
correlation which helps to engineer the extended eigenfunctions and determine
the band positions at will.
