ELECTRONIC-PROPERTIES AND MULTIFRACTALITY OF A ONE-DIMENSIONAL HIERARCHICAL SYSTEM IN THE PRESENCE OF AN ELECTRIC-FIELD

We study the influence of an applied electric field F on the electroni c properties of a one-dimensional system with hierarchical potential s trengths. By the method of the Poincare map, we calculate the transmis sion coefficient T as a function of the system size N. For small field s, it shows an algebraically localized behavior. With increasing field strength, a delocalization of the field-induced localized states occu rs and T shows extended behavior for R < 2 while it retains a power-la w localized behavior for R > 2. We perform a multifractal analysis on the wave functions of the field-induced states and find the multifract al property in the field-induced extended states.