Cauchy-perturbative matching and outer boundary conditions: computational studies

We present results from a new technique which allows extraction of gravitational radiation information from a generic three-dimensional numerical relativity code and provides stable outer boundary conditions. In our approach we match the solution of a Cauchy evolution of the nonlinear Einstein field equations to a set of one-dimensional linear equations obtained through perturbation techniques over a curved background. We discuss the validity of this approach in the case of linear and mildly nonlinear gravitational waves and show how a numerical module developed for this purpose is able to provide an accurate and numerically convergent description of the gravitational wave propagation and a stable numerical evolution.Comment: 20 pages, RevTe

Weak-localization and rectification current in non-diffusive quantum wires

We show that electron transport in disordered quantum wires can be described by a modified Cooperon equation, which coincides in form with the Dirac equation for the massive fermions in a 1+1 dimensional system. In this new formalism, we calculate the DC electric current induced by electromagnetic fields in quasi-one-dimensional rings. This current changes sign, from diamagnetic to paramagnetic, depending on the amplitude and frequency of the time-dependent external electromagnetic field.Comment: changed title, added more detail, to appear in J. Phys.: Condens. Matte

Cauchy-perturbative matching and outer boundary conditions I: Methods and tests

We present a new method of extracting gravitational radiation from three-dimensional numerical relativity codes and providing outer boundary conditions. Our approach matches the solution of a Cauchy evolution of Einstein's equations to a set of one-dimensional linear wave equations on a curved background. We illustrate the mathematical properties of our approach and discuss a numerical module we have constructed for this purpose. This module implements the perturbative matching approach in connection with a generic three-dimensional numerical relativity simulation. Tests of its accuracy and second-order convergence are presented with analytic linear wave data.Comment: 13 pages, 6 figures, RevTe

The collision of boosted black holes

We study the radiation from a collision of black holes with equal and opposite linear momenta. Results are presented from a full numerical relativity treatment and are compared with the results from a ``close-slow'' approximation. The agreement is remarkable, and suggests several insights about the generation of gravitational radiation in black hole collisions.Comment: 8 pages, RevTeX, 3 figures included with eps

Ground state of a partially melted Wigner molecule

We consider three spinless fermions free to move on 2d square lattice with periodic boundary conditions and interacting via a U/r Coulomb repulsion. When the Coulomb energy to kinetic energy ratio r_s is large, a rigid Wigner molecule is formed. As r_s decreases, we show that melting proceeds via an intermediate regime where a floppy two particle molecule coexists with a partially delocalized particle. A simple ansatz is given to describe the ground state of this mesoscopic solid-liquid regime.Comment: to appear in Europhysics Letter

Waveform propagation in black hole spacetimes: evaluating the quality of numerical solutions

We compute the propagation and scattering of linear gravitational waves off a Schwarzschild black hole using a numerical code which solves a generalization of the Zerilli equation to a three dimensional cartesian coordinate system. Since the solution to this problem is well understood it represents a very good testbed for evaluating our ability to perform three dimensional computations of gravitational waves in spacetimes in which a black hole event horizon is present.Comment: 13 pages, RevTeX, to appear in Phys. Rev.

The Evolution of Distorted Rotating Black Holes II: Dynamics and Analysis

We have developed a numerical code to study the evolution of distorted, rotating black holes. This code is used to evolve a new family of black hole initial data sets corresponding to distorted ``Kerr'' holes with a wide range of rotation parameters, and distorted Schwarzschild black holes with odd-parity radiation. Rotating black holes with rotation parameters as high as $a/m=0.87$ are evolved and analyzed in this paper. The evolutions are generally carried out to about $t=100M$, where $M$ is the ADM mass. We have extracted both the even- and odd-parity gravitational waveforms, and find the quasinormal modes of the holes to be excited in all cases. We also track the apparent horizons of the black holes, and find them to be a useful tool for interpreting the numerical results. We are able to compute the masses of the black holes from the measurements of their apparent horizons, as well as the total energy radiated and find their sum to be in excellent agreement with the ADM mass.Comment: 26 pages, LaTeX with RevTeX 3.0 macros. 27 uuencoded gz-compressed postscript figures. Also available at http://jean-luc.ncsa.uiuc.edu/Papers/ Submitted to Physical Review

Collisions of boosted black holes: perturbation theory prediction of gravitational radiation

We consider general relativistic Cauchy data representing two nonspinning, equal-mass black holes boosted toward each other. When the black holes are close enough to each other and their momentum is sufficiently high, an encompassing apparent horizon is present so the system can be viewed as a single, perturbed black hole. We employ gauge-invariant perturbation theory, and integrate the Zerilli equation to analyze these time-asymmetric data sets and compute gravitational wave forms and emitted energies. When coupled with a simple Newtonian analysis of the infall trajectory, we find striking agreement between the perturbation calculation of emitted energies and the results of fully general relativistic numerical simulations of time-symmetric initial data.Comment: 5 pages (RevTex 3.0 with 3 uuencoded figures), CRSR-107

Gravitational wave extraction and outer boundary conditions by perturbative matching

We present a method for extracting gravitational radiation from a three-dimensional numerical relativity simulation and, using the extracted data, to provide outer boundary conditions. The method treats dynamical gravitational variables as nonspherical perturbations of Schwarzschild geometry. We discuss a code which implements this method and present results of tests which have been performed with a three dimensional numerical relativity code

Superconducting Quantum Critical Point

We study the properties of a quantum critical point which develops in a BCS superconductor when pair-breaking suppresses the transition temperature to zero. The pair fluctuations are characterized by a dynamical critical exponent z=2. Except for very low temperatures, anomalous contribution to the conductivity is proportional to the square root of T in three dimensions, but to 1/T in two dimensions. At lowest temperatures, the conductivity correction varies as T to the power 1/4 in three dimensions, and as ln(1/T) in two.Comment: 3 pages, 3 Postscript figures, Late