We study electronic diffusion in quasi-one-dimensional systems with randomly placed interchain single and double bond cross-links corresponding to one and two adjacent interchain hoppings, respectively. While in the single bond case all states are localized, for the double bond case many completely unscattered states are obtained forming a "dilute" conducting band which leads to superdiffusive wave packet dynamics. This new type of band structure can explain the unusual transport properties of highly conducting polymers.

We carry out an exact calculation of the transmission of electrons through a quantum dot in the Coulomb blockade regime for both degenerate and nondegenerate cases. We show that the intrinsic interference among the paths produced by the states of the dot causes the phase coherence of adjacent resonant peaks. The expression of conductance obtained in the degenerate case reproduces the main features of a dot in the Kondo regime.

Localization-delocalization transition in disordered quantum small-world network model is confirmed by using the numerical multifractal analysis of the wave functions at the critical point. A linear relation between the numerator and the denominator of the parametric representation for the singularity spectrum of the wave functions near the transition point is obtained, serving as a criterion of the critical behavior. The singularity spectrum f (α) at the critical point is size independent. The variation of the fractal intensityαq at q50 and q51 in changing the rewiring probability p reveals the phase transition as shown in the level statistics on the same model.

We investigate the dephasing of electron wave functions due to interaction with a two-level system (TLS) in a quantum dot. It is found that if the TLS is intimately coupled to the electron rather than being in equilibrium with the thermal bath, the ground state of the whole system is a many-body state with nonzero amplitudes for the TLS being at the higher level. By averaging over the TLS degree of freedom a finite dephasing rate of the pure electron states at zero temperature is obtained. From this we discuss the conditions for observing the saturation of the dephasing rate at low temperatures.

We investigate the resonant transmission of electrons through a multilevel quantum in the Coulomb blockade regime. We show that the quantum interference between the path through the resonant level and the paths via other (nonresonant) levels results in the Fano asymmetry of the transmission peaks. The Fano parameter q is expressed in terms of the level spacing and the dot-lead coupling. The Coulomb blockade provides another origin of asymmetry for the resonances of the conductance due to the asymmetric occupation about a resonant point. Physical ingredients that influence these two mechanisms of the asymmetry are discussed.