1,678 research outputs found
Do the Barker Codes End?
A Barker code is a binary code with k^th autocorrelation <= 1 for all nonzero k.
At the workshop, the Barker code group split into four non-disjoint subgroups:
- An "algebra group", who explored symmetries of the search space that preserve the autocorrelations' magnitude.
- A "computing group", who explored methods for quickly finding binary codes with very good autocorrelation properties.
- A "statistics group", who explored ways to quantify what has been empirically observed about autocorrelation in the search space S_2^N.
- A "continuous group", who explored a non-discrete analogue of the problem of finding sequences with good autocorrelations
Effect of Ordering on Spinodal Decomposition of Liquid-Crystal/Polymer Mixtures
Partially phase-separated liquid-crystal/polymer dispersions display highly
fibrillar domain morphologies that are dramatically different from the typical
structures found in isotropic mixtures. To explain this, we numerically explore
the coupling between phase ordering and phase separation kinetics in model
two-dimensional fluid mixtures phase separating into a nematic phase, rich in
liquid crystal, coexisting with an isotropic phase, rich in polymer. We find
that phase ordering can lead to fibrillar networks of the minority polymer-rich
phase
Edge reconstruction in the fractional quantum Hall regime
The interplay of electron-electron interaction and confining potential can
lead to the reconstruction of fractional quantum Hall edges. We have performed
exact diagonalization studies on microscopic models of fractional quantum Hall
liquids, in finite size systems with disk geometry, and found numerical
evidence of edge reconstruction under rather general conditions. In the present
work we have taken into account effects like layer thickness and Landau level
mixing, which are found to be of quantitative importance in edge physics. Due
to edge reconstruction, additional nonchiral edge modes arise for both
incompressible and compressible states. These additional modes couple to
electromagnetic fields and thus can be detected in microwave conductivity
measurements. They are also expected to affect the exponent of electron Green's
function, which has been measured in tunneling experiments. We have studied in
this work the electric dipole spectral function that is directly related to the
microwave conductivity measurement. Our results are consistent with the
enhanced microwave conductivity observed in experiments performed on samples
with an array of antidots at low temperatures, and its suppression at higher
temperatures. We also discuss the effects of the edge reconstruction on the
single electron spectral function at the edge.Comment: 19 pages, 12 figure
The fermi arc and fermi pocket in cuprates in a short-range diagonal stripe phase
In this paper we studied the fermi arc and the fermi pocket in cuprates in a
short-range diagonal stripe phase with wave vectors , which
reproduce with a high accuracy the positions and sizes of the fermi arc and
fermi pocket and the superstructure in cuprates observed by Meng et
al\cite{Meng}. The low-energy spectral function indicates that the fermi pocket
results from the main band and the shadow band at the fermi energy. Above the
fermi energy the shadow band gradually departs away from the main band, leaving
a fermi arc. Thus we conclude that the fermi arc and fermi pocket can be fully
attributed to the stripe phase but has nothing to do with pairing.
Incorporating a d-wave pairing potential in the stripe phase the spectral
weight in the antinodal region is removed, leaving a clean fermi pocket in the
nodal region.Comment: 5 pages, 6 figure
Spin chains with dynamical lattice supersymmetry
Spin chains with exact supersymmetry on finite one-dimensional lattices are
considered. The supercharges are nilpotent operators on the lattice of
dynamical nature: they change the number of sites. A local criterion for the
nilpotency on periodic lattices is formulated. Any of its solutions leads to a
supersymmetric spin chain. It is shown that a class of special solutions at
arbitrary spin gives the lattice equivalents of the N=(2,2) superconformal
minimal models. The case of spin one is investigated in detail: in particular,
it is shown that the Fateev-Zamolodchikov chain and its off-critical extension
admits a lattice supersymmetry for all its coupling constants. Its
supersymmetry singlets are thoroughly analysed, and a relation between their
components and the weighted enumeration of alternating sign matrices is
conjectured.Comment: Revised version, 52 pages, 2 figure
A Gravitational Aharonov-Bohm Effect, and its Connection to Parametric Oscillators and Gravitational Radiation
A thought experiment is proposed to demonstrate the existence of a
gravitational, vector Aharonov-Bohm effect. A connection is made between the
gravitational, vector Aharonov-Bohm effect and the principle of local gauge
invariance for nonrelativistic quantum matter interacting with weak
gravitational fields. The compensating vector fields that are necessitated by
this local gauge principle are shown to be incorporated by the DeWitt minimal
coupling rule. The nonrelativistic Hamiltonian for weak, time-independent
fields interacting with quantum matter is then extended to time-dependent
fields, and applied to problem of the interaction of radiation with
macroscopically coherent quantum systems, including the problem of
gravitational radiation interacting with superconductors. But first we examine
the interaction of EM radiation with superconductors in a parametric oscillator
consisting of a superconducting wire placed at the center of a high Q
superconducting cavity driven by pump microwaves. We find that the threshold
for parametric oscillation for EM microwave generation is much lower for the
separated configuration than the unseparated one, which then leads to an
observable dynamical Casimir effect. We speculate that a separated parametric
oscillator for generating coherent GR microwaves could also be built.Comment: 25 pages, 5 figures, YA80 conference (Chapman University, 2012
Origin and evolution of the light nuclides
After a short historical (and highly subjective) introduction to the field, I
discuss our current understanding of the origin and evolution of the light
nuclides D, He-3, He-4, Li-6, Li-7, Be-9, B-10 and B-11. Despite considerable
observational and theoretical progress, important uncertainties still persist
for each and every one of those nuclides. The present-day abundance of D in the
local interstellar medium is currently uncertain, making it difficult to infer
the recent chemical evolution of the solar neighborhood. To account for the
observed quasi-constancy of He-3 abundance from the Big Bang to our days, the
stellar production of that nuclide must be negligible; however, the scarce
observations of its abundance in planetary nebulae seem to contradict this
idea. The observed Be and B evolution as primaries suggests that the source
composition of cosmic rays has remained quasi-constant since the early days of
the Galaxy, a suggestion with far reaching implications for the origin of
cosmic rays; however, the main idea proposed to account for that constancy,
namely that superbubbles are at the source of cosmic rays, encounters some
serious difficulties. The best explanation for the mismatch between primordial
Li and the observed "Spite-plateau" in halo stars appears to be depletion of Li
in stellar envelopes, by some yet poorly understood mechanism. But this
explanation impacts on the level of the recently discovered early ``Li-6
plateau'', which (if confirmed), seriously challenges current ideas of cosmic
ray nucleosynthesis.Comment: 18 pages, 9 figs. Invited Review in "Symposium on the Composition of
Matter", honoring Johannes Geiss on the occasion of his 80th birthday
(Grindelwald, Switzerland, Sept. 2006), to be published in Space Science
Series of ISS
An angle-resolved photoemission spectral function analysis of the electron doped cuprate Nd_1.85Ce_0.15CuO_4
Using methods made possible by recent advances in photoemission technology,
we perform an indepth line-shape analysis of the angle-resolved photoemission
spectra of the electron doped (n-type) cuprate superconductor
Nd_1.85Ce_0.15CuO_4. Unlike for the p-type materials, we only observe weak mass
renormalizations near 50-70 meV. This may be indicative of smaller
electron-phonon coupling or due to the masking effects of other interactions
that make the electron-phonon coupling harder to detect. This latter scenario
may suggest limitations of the spectral function analysis in extracting
electronic self-energies when some of the interactions are highly momentum
dependent.Comment: 8 pages, 5 figure
On the Quasi-Linear Elliptic PDE in Physics and Geometry
It is shown that for each finite number of Dirac measures supported at points
in three-dimensional Euclidean space, with given amplitudes , there
exists a unique real-valued Lipschitz function , vanishing at infinity,
which distributionally solves the quasi-linear elliptic partial differential
equation of divergence form
. Moreover, is real analytic away from the . The result
can be interpreted in at least two ways: (a) for any number of point charges of
arbitrary magnitude and sign at prescribed locations in three-dimensional
Euclidean space there exists a unique electrostatic field which satisfies the
Maxwell-Born-Infeld field equations smoothly away from the point charges and
vanishes as ; (b) for any number of integral mean curvatures
assigned to locations there exists a unique asymptotically flat, almost
everywhere space-like maximal slice with point defects of Minkowski spacetime,
having lightcone singularities over the but being smooth otherwise, and
whose height function vanishes as . No struts between the point
singularities ever occur.Comment: This is the preprint of the version published in 2012 in Commun.
Math. Phys. PLUS an errata which has been accepted 08/13/2018 for publication
in Commun. Math. Phy
Spanning forests and the q-state Potts model in the limit q \to 0
We study the q-state Potts model with nearest-neighbor coupling v=e^{\beta
J}-1 in the limit q,v \to 0 with the ratio w = v/q held fixed. Combinatorially,
this limit gives rise to the generating polynomial of spanning forests;
physically, it provides information about the Potts-model phase diagram in the
neighborhood of (q,v) = (0,0). We have studied this model on the square and
triangular lattices, using a transfer-matrix approach at both real and complex
values of w. For both lattices, we have computed the symbolic transfer matrices
for cylindrical strips of widths 2 \le L \le 10, as well as the limiting curves
of partition-function zeros in the complex w-plane. For real w, we find two
distinct phases separated by a transition point w=w_0, where w_0 = -1/4 (resp.
w_0 = -0.1753 \pm 0.0002) for the square (resp. triangular) lattice. For w >
w_0 we find a non-critical disordered phase, while for w < w_0 our results are
compatible with a massless Berker-Kadanoff phase with conformal charge c = -2
and leading thermal scaling dimension x_{T,1} = 2 (marginal operator). At w =
w_0 we find a "first-order critical point": the first derivative of the free
energy is discontinuous at w_0, while the correlation length diverges as w
\downarrow w_0 (and is infinite at w = w_0). The critical behavior at w = w_0
seems to be the same for both lattices and it differs from that of the
Berker-Kadanoff phase: our results suggest that the conformal charge is c = -1,
the leading thermal scaling dimension is x_{T,1} = 0, and the critical
exponents are \nu = 1/d = 1/2 and \alpha = 1.Comment: 131 pages (LaTeX2e). Includes tex file, three sty files, and 65
Postscript figures. Also included are Mathematica files forests_sq_2-9P.m and
forests_tri_2-9P.m. Final journal versio
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