Level-spacing distribution of a fractal matrix

We diagonalize numerically a Fibonacci matrix with fractal Hilbert space st ructure of dimension d(f) = 1.8316.... We show that the density of states i s logarithmically normal while the corresponding level-statistics can be de scribed as critical since the nearest-neighbor distribution function approa ches the intermediate semi-Poisson curve. We find that the eigenvector ampl itudes of this matrix are also critical lying between extended and localize d. (C) 2001 Elsevier Science B.V. All rights reserved.