2 INTERACTING ELECTRONS IN A QUASI-PERIODIC CHAIN

We study numerically the effect of on-site Hubbard interaction U betwe en two electrons in the quasiperiodic Harper's equation. In the period ic chain limit, by mapping the problem to that of one electron in two dimensions with a diagonal line of impurities of strength U we demonst rate a band of resonance two-particle pairing states starting from E=U . In the ballistic (metallic) regime we show explicitly interaction-as sisted extended pairing states and multifractal pairing states in the diffusive (critical) regime. We also obtain localized pairing states i n the gaps and the created subband due to U, whose number increases wh en going to the localized regime, which are responsible for reducing t he velocity and the diffusion coefficient in the qualitatively similar to the noninteracting case ballistic and diffusive two-particle dynam ics. In the localized regime we find propagation enhancement for small U and stronger localization for larger U, as in disordered systems.