Statistical analysis of a multiplytwisted helix
Abstract
A multiplytwisted helix, in which a onedimensional array of components is twisted, producing a helix which if twisted itself produces a doublytwisted helix, and so on, in which there are couplings between adjacent rounds of helices, was investigated using a cellular automaton and the spectral statistics of a quantum particle. A useful distance between the components of the structure is measured using a cellular automaton, the dynamics of which is simulated for a number of initial conditions in order to determine the degree of connectivity between the components. The area of the sphere with radius r, on the basis of the above distance, is shown to be proportional to r^{2} when r is small. The Anderson transition was investigated based on the spectral statistics of a quantum particle in a multiplytwisted helix with onsite random potentials. As the strength of the onsite random potentials increases, the Anderson transition occurs. Both results support our conclusion that the number of dimensions is always three for every multiplytwisted helix if the couplings between adjacent rounds are strong enough.
 Publication:

Physica A Statistical Mechanics and its Applications
 Pub Date:
 March 2001
 DOI:
 10.1016/S03784371(00)005720
 Bibcode:
 2001PhyA..292..437U