Abstract
The energy spectrum of single- and two-particle excitations for a one-dimensional aperiodic Fibonacci sequence of quantum dots (QDs) was determined within the pair interaction approximation. The critical behaviour of the energy spectrum and wave functions were obtained. The energy spectrum is a Cantor set of zero Lebesgue measure. The perturbation theory was used to obtain the critical value of the distance between the centres of the neighboring QDs when the first-order corrections to the energy of the excitations were neglected. The contribution of the external transverse magnetic field to particle localization was also considered and the influence of the external field on the first-order corrections to the energy was analyzed. The transmission coefficient was determined using the quasi-classical approximation and the energy level splitting versus the distance between the QDs was obtained. The effect of resonance tunneling of the excitations between QD pairs was studied. Localization occurs at finite values of the perturbations, in contrast to periodic one-dimensional sequences.
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