Single-and two-particle excitations in aperiodic sequences of quantum dots

The critical behavior of single-and two-particle excitation energy spectrum in aperiodic sequences of quantum dots was investigated by the level statistics method in the pair interaction approximation. Fibonacci, Thu-Morse, Cantor and double-period aperiodic sequences were studied. Using the perturbation theory it was shown that the localization of the excitations occurs at the finite degrees of perturbation. The transverse magnetic field effects on the localization of excitations, and the effective steepness parameter of confining potential is revealed. The resonance tunneling of excitations between neighboring quantum dots with or without phonon emission was studied using the nonstationary perturbation theory. The single-and two-particle transport in time dependent external field was analyzed, and the transmission probabilities and average current of the particles in the limit of a weak wire-lead coupling were estimated.