1,776 research outputs found
Applying black hole perturbation theory to numerically generated spacetimes
Nonspherical perturbation theory has been necessary to understand the meaning
of radiation in spacetimes generated through fully nonlinear numerical
relativity. Recently, perturbation techniques have been found to be successful
for the time evolution of initial data found by nonlinear methods. Anticipating
that such an approach will prove useful in a variety of problems, we give here
both the practical steps, and a discussion of the underlying theory, for taking
numerically generated data on an initial hypersurface as initial value data and
extracting data that can be considered to be nonspherical perturbations.Comment: 14 pages, revtex3.0, 5 figure
Critical behavior at Mott-Anderson transition: a TMT-DMFT perspective
We present a detailed analysis of the critical behavior close to the
Mott-Anderson transition. Our findings are based on a combination of numerical
and analytical results obtained within the framework of Typical-Medium Theory
(TMT-DMFT) - the simplest extension of dynamical mean field theory (DMFT)
capable of incorporating Anderson localization effects. By making use of
previous scaling studies of Anderson impurity models close to the
metal-insulator transition, we solve this problem analytically and reveal the
dependence of the critical behavior on the particle-hole symmetry. Our main
result is that, for sufficiently strong disorder, the Mott-Anderson transition
is characterized by a precisely defined two-fluid behavior, in which only a
fraction of the electrons undergo a "site selective" Mott localization; the
rest become Anderson-localized quasiparticles.Comment: 4+ pages, 4 figures, v2: minor changes, accepted for publication in
Phys. Rev. Let
Black hole collisions from Brill-Lindquist initial data: predictions of perturbation theory
The Misner initial value solution for two momentarily stationary black holes
has been the focus of much numerical study. We report here analytic results for
an astrophysically similar initial solution, that of Brill and Lindquist (BL).
Results are given from perturbation theory for initially close holes and are
compared with available numerical results. A comparison is made of the
radiation generated from the BL and the Misner initial values, and the physical
meaning is discussed.Comment: 11 pages, revtex3.0, 5 figure
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.
Superconducting RF Metamaterials Made with Magnetically Active Planar Spirals
Superconducting metamaterials combine the advantages of low-loss, large
inductance (with the addition of kinetic inductance), and extreme tunability
compared to their normal metal counterparts. Therefore, they allow realization
of compact designs operating at low frequencies. We have recently developed
radio frequency (RF) metamaterials with a high loaded quality factor and an
electrical size as small as 658, ( is the free space
wavelength) by using Nb thin films. The RF metamaterial is composed of truly
planar spirals patterned with lithographic techniques. Linear transmission
characteristics of these metamaterials show robust Lorentzian resonant peaks in
the sub- 100 MHz frequency range below the of Nb. Though Nb is a
non-magnetic material, the circulating currents in the spirals generated by RF
signals produce a strong magnetic response, which can be tuned sensitively
either by temperature or magnetic field thanks to the superconducting nature of
the design. We have also observed strong nonlinearity and meta-stable jumps in
the transmission data with increasing RF input power until the Nb is driven
into the normal state. We discuss the factors modifying the induced magnetic
response from single and 1-D arrays of spirals in the light of numerical
simulations.Comment: 4 pages, 7 figure
Head--on Collision of Two Unequal Mass Black Holes
We present results from the first fully nonlinear numerical calculations of
the head--on collision of two unequal mass black holes. Selected waveforms of
the most dominant l=2, 3 and 4 quasinormal modes are shown, as are the total
radiated energies and recoil velocities for a range of mass ratios and initial
separations. Our results validate the close and distant separation limit
perturbation studies, and suggest that the head--on collision scenario is not
likely to produce an astrophysically significant recoil effect.Comment: 5 pages, 3 figure
Head-on collision of unequal mass black holes: close-limit predictions
The close-limit method has given approximations in excellent agreement with
those of numerical relativity for collisions of equal mass black holes. We
consider here colliding holes with unequal mass, for which numerical relativity
results are not available. We try to ask two questions: (i) Can we get
approximate answers to astrophysical questions (ideal mass ratio for energy
production, maximum recoil velocity, etc.), and (ii) can we better understand
the limitations of approximation methods. There is some success in answering
the first type of question, but more with the second, especially in connection
with the issue of measures of the intrinsic mass of the colliding holes, and of
the range of validity of the method.Comment: 19 pages, RevTeX + 9 postscript figure
Statistics of anomalously localized states at the center of band E=0 in the one-dimensional Anderson localization model
We consider the distribution function of the eigenfunction
amplitude at the center-of-band (E=0) anomaly in the one-dimensional
tight-binding chain with weak uncorrelated on-site disorder (the
one-dimensional Anderson model). The special emphasis is on the probability of
the anomalously localized states (ALS) with much larger than the
inverse typical localization length . Using the solution to the
generating function found recently in our works we find the
ALS probability distribution at . As
an auxiliary preliminary step we found the asymptotic form of the generating
function at which can be used to compute other
statistical properties at the center-of-band anomaly. We show that at
moderately large values of , the probability of ALS at E=0
is smaller than at energies away from the anomaly. However, at very large
values of , the tendency is inverted: it is exponentially
easier to create a very strongly localized state at E=0 than at energies away
from the anomaly. We also found the leading term in the behavior of
at small and show that it is
consistent with the exponential localization corresponding to the Lyapunov
exponent found earlier by Kappus and Wegner and Derrida and Gardner.Comment: 25 pages, 9 figure
Continuous Self-Similarity Breaking in Critical Collapse
This paper studies near-critical evolution of the spherically symmetric
scalar field configurations close to the continuously self-similar solution.
Using analytic perturbative methods, it is shown that a generic growing
perturbation departs from the critical Roberts solution in a universal way. We
argue that in the course of its evolution, initial continuous self-similarity
of the background is broken into discrete self-similarity with echoing period
, reproducing the symmetries of the critical
Choptuik solution.Comment: RevTeX 3.1, 28 pages, 5 figures; discussion rewritten to clarify
several issue
Interactions and Scaling in a Disordered Two-Dimensional Metal
We show that a non-Fermi liquid state of interacting electrons in two
dimensions is stable in the presence of disorder and is a perfect conductor,
provided the interactions are sufficiently strong. Otherwise, the disorder
leads to localization as in the case of non-interacting electrons. This
conclusion is established by examining the replica field theory in the weak
disorder limit, but in the presence of arbitrary electron-electron interaction.
Thus, a disordered two-dimensional metal is a perfect metal, but not a Fermi
liquid.Comment: 4 pages, RevTe
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