PROPERTY OF FIBONACCI NUMBERS AND THE PERIODICLIKE PERFECTLY TRANSPARENT ELECTRONIC STATES IN FIBONACCI CHAINS

We study the properties of Fibonacci numbers and the transparency of c lusters for electrons at some values of the energy. For the mth Fibona cci number F-m, a set of divisors are obtained by F-m/k = right perpen dicular F-m/k left perpendicular, 1 < k less than or equal to F-m. Int erestingly, the numerical and analytical results show that any new div isors of the mth Fibonacci sequence will appear periodically in the fo llowing I:Fibonacci sequence. Furthermore, in the mixing Fibonacci sys tem, we perform computer simulations and analytical calculations to st udy the transparent properties and spatial distributions of electronic states with the energies determined by the divisors of Fibonacci syst ems. The results show that the transmission coefficients are unity and the corresponding wave functions have periodic-like features. We repo rt that an infinite number of one-dimensional disordered lattices, whi ch an composed of some specific Fibonacci clusters, exhibit an absence of localization. [S0163-1829(98)04325-2].