Collective charge density wave motion through an ensemble of Aharonov-Bohm rings

We investigate theoretically the collective charge density wave motion through an ensemble of small disordered Aharonov-Bohm rings. It is shown that the magnetic flux modulates the threshold field and the magnetoresistance with a half flux quantum periodicity $\Phi_{0}/2=h/2e$, resulting from ensemble averaging over random scattering phases of multiple rings. The magnitude of the magnetoresistance oscillations decreases rapidly with increasing bias. This is consistent with recent experiments on $NbSe_3$ in presence of columnar defects [Phys. Rev. Lett. 78, 919 (1997)].Comment: 4 pages Revtex, 2 figures. Submitted to Phys. Rev. Let

Strong Effects of Weak Localization in Charge Density Wave/Normal Metal Hybrids

Collective transport through a multichannel disordered conductor in contact with charge-density-wave electrodes is theoretically investigated. The statistical distribution function of the threshold potential for charge-density wave sliding is calculated by random matrix theory. In the diffusive regime weak localization has a strong effect on the sliding motion.Comment: To be published in Physical Review

Random-Matrix Theory of Parametric Correlations in the Spectra of Disordered Metals and Chaotic Billiards

We study the response to an external perturbation of the energy levels of a disordered metallic particle, by means of the Brownian-motion model introduced by Dyson in the theory of random matrices, and reproduce the results of a recent microscopic theory of Altshuler, Simons, and Szafer. This establishes the validity of Dyson's basic assumption, that parametric correlations in the energy spectrum are dominated by level repulsion, and therefore solely dependent on the symmetry of the hamiltonian. ***Submitted to Physica A.****Comment: 24 pages, REVTeX-3.0, INLO-PUB-931028

Conductance length autocorrelation in quasi one-dimensional disordered wires

Employing techniques recently developed in the context of the Fokker--Planck approach to electron transport in disordered systems we calculate the conductance length correlation function $$ for quasi 1d wires. Our result is valid for arbitrary lengths L and $\Delta L$. In the metallic limit the correlation function is given by a squared Lorentzian. In the localized regime it decays exponentially in both L and $\Delta L$. The correlation length is proportional to L in the metallic regime and saturates at a value approximately given by the localization length $\xi$ as $L\gg\xi$.Comment: 23 pages, Revtex, two figure

Origin of Magic Angular Momentum in a Quantum Dot under Strong Magnetic Field

This paper investigates origin of the extra stability associated with particular values (magic numbers) of the total angular momentum of electrons in a quantum dot under strong magnetic field. The ground-state energy, distribution functions of density and angular momentum, and pair correlation function are calculated in the strong field limit by numerical diagonalization of the system containing up to seven electrons. It is shown that the composite fermion picture explains the small magic numbers well, while a simple geometrical picture does better as the magic number increases. Combination of these two pictures leads to identification of all the magic numbers. Relation of the magic-number states to the Wigner crystal and the fractional quantum Hall state is discussed.Comment: 12 pages, 9 Postscript figures, uses jpsj.st

Scaling Theory of Conduction Through a Normal-Superconductor Microbridge

The length dependence is computed of the resistance of a disordered normal-metal wire attached to a superconductor. The scaling of the transmission eigenvalue distribution with length is obtained exactly in the metallic limit, by a transformation onto the isobaric flow of a two-dimensional ideal fluid. The resistance has a minimum for lengths near l/Gamma, with l the mean free path and Gamma the transmittance of the superconductor interface.Comment: 8 pages, REVTeX-3.0, 3 postscript figures appended as self-extracting archive, INLO-PUB-94031

Magnetolocalization in disordered quantum wires

The magnetic field dependent localization in a disordered quantum wire is considered nonperturbatively. An increase of an averaged localization length with the magnetic field is found, saturating at twice its value without magnetic field. The crossover behavior is shown to be governed both in the weak and strong localization regime by the magnetic diffusion length L_B. This function is derived analytically in closed form as a function of the ratio of the mean free path l, the wire thickness W, and the magnetic length l_B for a two-dimensional wire with specular boundary conditions, as well as for a parabolic wire. The applicability of the analytical formulas to resistance measurements in the strong localization regime is discussed. A comparison with recent experimental results on magnetolocalization is included.Comment: 22 pages, RevTe

Dimensional Crossover of Localisation and Delocalisation in a Quantum Hall Bar

The 2-- to 1--dimensional crossover of the localisation length of electrons confined to a disordered quantum wire of finite width $L_y$ is studied in a model of electrons moving in the potential of uncorrelated impurities. An analytical formula for the localisation length is derived, describing the dimensional crossover as function of width $L_y$, conductance $g$ and perpendicular magnetic field $B$ . On the basis of these results, the scaling analysis of the quantum Hall effect in high Landau levels, and the delocalisation transition in a quantum Hall wire are reconsidered.Comment: 12 pages, 7 figure

Non-perturbative calculation of the probability distribution of plane-wave transmission through a disordered waveguide

A non-perturbative random-matrix theory is applied to the transmission of a monochromatic scalar wave through a disordered waveguide. The probability distributions of the transmittances T_{mn} and T_n=\sum_m T_{mn} of an incident mode n are calculated in the thick-waveguide limit, for broken time-reversal symmetry. A crossover occurs from Rayleigh or Gaussian statistics in the diffusive regime to lognormal statistics in the localized regime. A qualitatively different crossover occurs if the disordered region is replaced by a chaotic cavity. ***Submitted to Physical Review E.***Comment: 7 pages, REVTeX-3.0, 5 postscript figures appended as self-extracting archive. A complete postscript file with figures and text (4 pages) is available from http://rulgm4.LeidenUniv.nl/preprints.htm