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The eigenstates and the scattering transmission for two interacting electrons are found exactly for I quantum dots, including the hybridization with the states on the leads. The results imply limitations on the validity of the Coulomb blockade picture. The ground states for I=1, and 2 on a one--dimensional chain (modeling single and double quantum dots) exhibit quantum delocalization and magnetic transitions. The effective transmission T of two interacting electrons through one impurity (I=1) is enhanced by a renormalization of the repulsive interaction, when one of the electrons is captured in a strongly localized state.

We describe the interaction of surface acoustic waves with electrons in an array of quantum wires, patterned out of a two dimensional electron gas. Two specific geometries are considered, in which the surface acoustic wave travels parallel, or perpendicular to the wires. Although we assume the electron wave functions in different wires do not overlap, the screening of the phonon potential by the electrons in the wire array is a collective phenomenon. It is shown that the surface acoustic wave absorption cannot be described via the ac conductivity in the usual manner. We derive an integral equation for the dielectric function of the electrons in the quantum wire system, and solve it in the narrow wire approximation. Using the dielectric function we find the absorption and the change in velocity of the surface acoustic waves., Comment: REVTeX, 8 pages, no figures

The interaction of a surface acoustic wave (SAW) with a a two-dimensional electron gas in a periodic electric potential and a classical magnetic field is considered. We calculate the attenuation of the SAW and its velocity change and show that these quantities exhibit Weiss oscillations., Comment: 4 pages REVTEX, 2 figures included as eps files

A recipe for the generalization of the Boltzmann equation to a quantum kinetic equation is given for cases in which only level shift and broadening are considered, while coherence phenomena can be neglected. We also consider a specific problem: Hot luminescence from a quantum wire near the threshold for optical phonon emission. The problem is first discussed within the framework of the Boltzmann equation. After pointing out the failure of this description, the Boltzmann equations are generalized to a set of quantum kinetic equations, which in turn are solved in order to describe the luminescence spectra., Comment: 35 pages, REVTeX, with 6 figures

The Hall conductivity and resistivity of strongly localized electrons at low temperatures and at small magnetic fields are obtained. It is found that the results depend on whether the conductivity or the resistivity tensors are averaged to obtain the macroscopic Hall resistivity. In the second case the Hall resistivity always {\it diverges} exponentially as the temperature tends to zero. But when the Hall resistivity is derived from the averaged conductivity, the resulting temperature dependence is sensitive to the disorder configuration. Then the Hall resistivity may approach a constant value as $T\to 0$. This is the Hall insulating behavior. It is argued that for strictly dc conditions, the transport quantity that should be averaged is the resistivity., Comment: Latex