Transmission through a Fibonacci chain Academic Article uri icon

abstract

  • We study transmission ||tN|| and reflection ||rN|| of a plane wave (with wave number k>0) through a one-dimensional array of N delta-function potentials with equal strengths v located on the Fibonacci chain sequence xn=n+u[n/tau], n=1,2,..,N (where u is an irrational number, tau=(1+ &surd;5 )/2, and [...] denotes the integer part thereof) in the limit N-->∞. Using analytical and number-theoretical methods, we arrive at the following results. (i) For any k, if v is large enough, the sequence of reflection coefficients ||rN|| has a subsequence that tends to unity. (ii) If k is an integer multiple of pi/u, then there is a threshold value v0 for v such that, if v>=v0, then ||rN||-->1 as N-->∞, whereas if v1 as N-->∞.

publication date

  • January 1, 1991