We study Coulomb drag in a pair of parallel one-dimensional electron systems within the framework of the Tomonaga-Luttinger model. We find that Coulomb coupling has a much stronger effect on one-dimensional wires than on two-dimensional layers: At zero temperature the transresistivity diverges, due to the formation of locked charge density waves. At temperature well above a crossover temperature T* the transresistivity follows a power law ϰT x , where the interaction-strength dependent exponent x is determined by the Luttinger liquid parameter K cϪ of the relative charge mode. At temperature below T* relative charge displacements are enabled by solitonic excitations, reflected by an exponential temperature dependence. The crossover temperature T* depends sensitively on the wire width, interwire distance, Fermi wavelength and the effective Bohr radius. For wire distances d ӷk FϪ1 it is exponentially suppressed with T*/E F ϳexp͓Ϫdk F /(1ϪK cϪ )͔. The behavior changes drastically if each of the two wires develop spin gaps. In this case we find that the transresistivity vanishes at zero temperature. We discuss our results in view of possible experimental realizations in GaAs-Al x Ga 1Ϫx As semiconductor structures.

We investigate numerically the localization-delocalization transition in quantum Hall systems with long-range disorder potential with respect to multifractal properties. Wave functions at the transition energy are obtained within the framework of the generalized Chalker-Coddington network model. We determine the critical exponent a. characterizing the scaling behaviour of the local order parameter for systems with potential correlation length d up to 12 magnetic lengths 1. Our results show that a. does not depend on the ratio d/l. With increasing d/l, effects due to classical percolation only cause an increase of the microscopic length scale, whereas the critical behaviour on larger scales remains unchanged. This proves that systems with long-range disorder belong to the same universality class as those with short-range disorder.

The Coulomb drag between two spatially separated one-dimensional (1D) electron systems in lithographically fabricated 2 µm long quantum wires is studied experimentally. The drag voltage V D shows peaks as a function of a gate voltage which shifts the position of the Fermi level relative to the 1D subbands. The maximum in V D and the drag resistance R D occurs when the 1D subbands of the wires are aligned and the Fermi wave vector is small. The drag resistance is found to decrease exponentially with interwire separation. In the temperature region 0.2 K T 1 K, R D decreases with increasing temperature in a power-law fashion R D ∝ T x with x ranging from −0.6 to −0.77 depending on the gate voltage. We interpret our data in terms of the Tomonaga-Luttinger liquid theory.

The spectral properties of a disordered electronic system at the metal-insulator transition point are investigated numerically. A recently derived relation between the anomalous diffusion exponent h and the spectral compressibility x at the mobility edge, x h͞2d, is confirmed for the integer quantum Hall delocalization transition. Our calculations are performed within the framework of a unitary network model and represent a new method to investigate spectral properties of disordered systems.[S0031-9007(97)

Within a generalized Caldeira-Leggett model, we analyze the conditions under which a bosonic heat bath can entangle two microscopic quantum systems at a distance r. We find that the attainable entanglement is extremely distance-sensitive. Significant entanglement can only be achieved if the systems are within a microscopic distance that is of order of the cutoff wavelength lambda of the system-bath interaction. At larger distances, the maximal entanglement is exponentially suppressed with a decay length of order lambda. We conclude that entanglement generation via a heat bath is not suitable for entangling remote objects.