Crossover of Level Statistics between Strong and Weak Localization in Two Dimensions

We investigate numerically the statistical properties of spectra of two-dimensional disordered systems by using the exact diagonalization and decimation method applied to the Anderson model. Statistics of spacings calculated for system sizes up to 1024 $\times$ 1024 lattice sites exhibits a crossover between Wigner and Poisson distributions. We perform a self-contained finite-size scaling analysis to find a single-valued one-parameter function $\gamma (L/\xi)$ which governs the crossover. The scaling parameter $\xi(W)$ is deduced and compared with the localization length. $\gamma ( L/\xi)$ does {\em not} show critical behavior and has two asymptotic regimes corresponding to weakly and strongly localized states.Comment: 4 pages in revtex, 3 postscript figure

Upper Bound on the Capacity of a Cascade of Nonlinear and Noisy Channels

An upper bound on the capacity of a cascade of nonlinear and noisy channels is presented. The cascade mimics the split-step Fourier method for computing waveform propagation governed by the stochastic generalized nonlinear Schroedinger equation. It is shown that the spectral efficiency of the cascade is at most log(1+SNR), where SNR is the receiver signal-to-noise ratio. The results may be applied to optical fiber channels. However, the definition of bandwidth is subtle and leaves open interpretations of the bound. Some of these interpretations are discussed.Comment: The main change is to define the noise as bandlimited already in (8) rather than before (15). This serves to clarify subsequent step

Crossover from critical orthogonal to critical unitary statistics at the Anderson transition

We report a novel scale-independent, Aharonov-Bohm flux controlled crossover from critical orthogonal to critical unitary statistics at the disorder induced metal insulator transition. Our numerical investigations show that at the critical point the level statistics are definitely distinct and determined by fundamental symmetries. The latter is similar to the behavior of the metallic phase known from random matrix theory. The Aharonov-Bohm flux dependent crossover is characteristic of the critical ensemble.Comment: 4 pages RevTeX, 4 epsf-figures included, to appear in Physical Review Letters (August 1996

Shock-resolved Navier–Stokes simulation of the Richtmyer–Meshkov instability start-up at a light–heavy interface

The single-mode Richtmyer–Meshkov instability is investigated using a first-order perturbation of the two-dimensional Navier–Stokes equations about a one-dimensional unsteady shock-resolved base flow. A feature-tracking local refinement scheme is used to fully resolve the viscous internal structure of the shock. This method captures perturbations on the shocks and their influence on the interface growth throughout the simulation, to accurately examine the start-up and early linear growth phases of the instability. Results are compared to analytic models of the instability, showing some agreement with predicted asymptotic growth rates towards the inviscid limit, but significant discrepancies are noted in the transient growth phase. Viscous effects are found to be inadequately predicted by existing models

Quantum theory of an atom laser originating from a Bose-Einstein condensate or a Fermi gas in the presence of gravity

We present a 3D quantum mechanical theory of radio-frequency outcoupled atom lasers from trapped atomic gases in the presence of the gravitational force. Predictions for the total outcoupling rate as a function of the radio-frequency and for the beam wave function are given. We establish a sum rule for the energy integrated outcoupling, which leads to a separate determination of the coupling strength between the atoms and the radiation field. For a non-interacting Bose-Einstein condensate analytic solutions are derived which are subsequently extended to include the effects of atomic interactions. The interactions enhance interference effects in the beam profile and modify the outcoupling rate of the atom laser. We provide a complete quantum mechanical solution which is in line with experimental findings and allows to determine the validity of commonly used approximative methods. We also extend the formalism to a fermionic atom laser and analyze the effect of superfluidity on the outcoupling of atoms.Comment: 13 pages, 8 figures, slightly expanded versio

A HIERARCHICAL BAYES APPROACH TO MODELING CHOICE DATA: A STUDY OF WETLAND RESTORATION PROGRAMS

This study examines the factors the influence the values and importance that landowners place on the attributes of voluntary wetland restoration programs. Choice-based conjoint analysis, a stated preference method, was used to estimate the marginal utilities and values for restoration program attributes for North Carolina landowners. Landowner preferences were estimated at individual and aggregate levels to examine the importance of modeling heterogeneous preferences. Choice modeling performed at both aggregate and individual levels demonstrated the information gains from a disaggregated approach.Research Methods/ Statistical Methods,