2,897 research outputs found
Twistor theory of hyper-K{\"a}hler metrics with hidden symmetries
We briefly review the hierarchy for the hyper-K\"ahler equations and define a
notion of symmetry for solutions of this hierarchy. A four-dimensional
hyper-K\"ahler metric admits a hidden symmetry if it embeds into a hierarchy
with a symmetry. It is shown that a hyper-K\"ahler metric admits a hidden
symmetry if it admits a certain Killing spinor. We show that if the hidden
symmetry is tri-holomorphic, then this is equivalent to requiring symmetry
along a higher time and the hidden symmetry determines a `twistor group' action
as introduced by Bielawski \cite{B00}. This leads to a construction for the
solution to the hierarchy in terms of linear equations and variants of the
generalised Legendre transform for the hyper-K\"ahler metric itself given by
Ivanov & Rocek \cite{IR96}. We show that the ALE spaces are examples of
hyper-K\"ahler metrics admitting three tri-holomorphic Killing spinors. These
metrics are in this sense analogous to the 'finite gap' solutions in soliton
theory. Finally we extend the concept of a hierarchy from that of \cite{DM00}
for the four-dimensional hyper-K\"ahler equations to a generalisation of the
conformal anti-self-duality equations and briefly discuss hidden symmetries for
these equations.Comment: Final version. To appear in the August 2003 special issue of JMP on
`Integrability, Topological Solitons, and Beyond
Scalar second order evolution equations possessing an irreducible sl-valued zero curvature representation
We find all scalar second order evolution equations possessing an
sl-valued zero curvature representation that is not reducible to a proper
subalgebra of sl. None of these zero-curvature representations admits a
parameter.Comment: 10 pages, requires nath.st
The dispersive self-dual Einstein equations and the Toda lattice
The Boyer-Finley equation, or -Toda equation is both a reduction
of the self-dual Einstein equations and the dispersionlesslimit of the
-Toda lattice equation. This suggests that there should be a dispersive
version of the self-dual Einstein equation which both contains the Toda lattice
equation and whose dispersionless limit is the familiar self-dual Einstein
equation. Such a system is studied in this paper. The results are achieved by
using a deformation, based on an associative -product, of the algebra
used in the study of the undeformed, or dispersionless,
equations.Comment: 11 pages, LaTeX. To appear: J. Phys.
Hydrodynamic reductions of the heavenly equation
We demonstrate that Pleba\'nski's first heavenly equation decouples in
infinitely many ways into a triple of commuting (1+1)-dimensional systems of
hydrodynamic type which satisfy the Egorov property. Solving these systems by
the generalized hodograph method, one can construct exact solutions of the
heavenly equation parametrized by arbitrary functions of a single variable. We
discuss explicit examples of hydrodynamic reductions associated with the
equations of one-dimensional nonlinear elasticity, linearly degenerate systems
and the equations of associativity.Comment: 14 page
ASCA Detection of Pulsed X-ray Emission from PSR J0631+1036
ASCA's long look at the 288 millisecond radio pulsar, PSR J0631+1036, reveals
coherent X-ray pulsation from this source for the first time. The source was
first detected in the serendipitous Einstein observation and later identified
as a radio pulsar. Possible pulsation in the gamma-ray band has been detected
from the CGRO EGRET data (Zepka, et al. 1996). The X-ray spectrum in the ASCA
band is characterized by a hard power-law type emission with a photon index of
about 2.3, when fitted with a single power-law function modified with
absorption. An additional blackbody component of about 0.14 keV increases the
quality of the spectral fit. The observed X-ray flux is 2.1e-13 ergs/s/cm2 in
the 1-10 keV band. We find that many characteristics of PSR J0631+1036 are
similar to those of middle-aged gamma-ray pulsars such as PSR B1055-52, PSR
B0633+17 (Geminga), and PSR B0656+14.Comment: To appear in ApJ Letter
Using the local density approximation and the LYP, BLYP, and B3LYP functionals within Reference--State One--Particle Density--Matrix Theory
For closed-shell systems, the local density approximation (LDA) and the LYP,
BLYP, and B3LYP functionals are shown to be compatible with reference-state
one-particle density-matrix theory, where this recently introduced formalism is
based on Brueckner-orbital theory and an energy functional that includes exact
exchange and a non-universal correlation-energy functional. The method is
demonstrated to reduce to a density functional theory when the
exchange-correlation energy-functional has a simplified form, i.e., its
integrand contains only the coordinates of two electron, say r1 and r2, and it
has a Dirac delta function -- delta(r1 - r2) -- as a factor. Since Brueckner
and Hartree--Fock orbitals are often very similar, any local exchange
functional that works well with Hartree--Fock theory is a reasonable
approximation with reference-state one-particle density-matrix theory. The LDA
approximation is also a reasonable approximation. However, the Colle--Salvetti
correlation-energy functional, and the LYP variant, are not ideal for the
method, since these are universal functionals. Nevertheless, they appear to
provide reasonable approximations. The B3LYP functional is derived using a
linear combination of two functionals: One is the BLYP functional; the other
uses exact exchange and a correlation-energy functional from the LDA.Comment: 26 Pages, 0 figures, RevTeX 4, Submitted to Mol. Phy
Joint searches between gravitational-wave interferometers and high-energy neutrino telescopes: science reach and analysis strategies
Many of the astrophysical sources and violent phenomena observed in our
Universe are potential emitters of gravitational waves (GWs) and high-energy
neutrinos (HENs). A network of GW detectors such as LIGO and Virgo can
determine the direction/time of GW bursts while the IceCube and ANTARES
neutrino telescopes can also provide accurate directional information for HEN
events. Requiring the consistency between both, totally independent, detection
channels shall enable new searches for cosmic events arriving from potential
common sources, of which many extra-galactic objects.Comment: 4 pages. To appear in the Proceedings of the 2d Heidelberg Workshop:
"High-Energy Gamma-rays and Neutrinos from Extra-Galactic Sources",
Heidelberg (Germany), January 13-16, 200
Possible Signatures of a Cold-Flow Disk from MUSE using a z=1 galaxy--quasar pair towards SDSSJ1422-0001
We use a background quasar to detect the presence of circum-galactic gas
around a low-mass star forming galaxy. Data from the new Multi Unit
Spectroscopic Explorer (MUSE) on the VLT show that the host galaxy has a
dust-corrected star-formation rate (SFR) of 4.70.2 Msun/yr, with no
companion down to 0.22 Msun/yr (5 ) within 240 kpc (30"). Using a
high-resolution spectrum (UVES) of the background quasar, which is fortuitously
aligned with the galaxy major axis (with an azimuth angle of only
), we find, in the gas kinematics traced by low-ionization lines,
distinct signatures consistent with those expected for a "cold flow disk"
extending at least 12 kpc (). We estimate the mass accretion
rate to be at least two to three times larger than the SFR,
using the geometric constraints from the IFU data and the HI column density of
obtained from a {\it HST}/COS NUV spectrum. From
a detailed analysis of the low-ionization lines (e.g. ZnII, CrII, TiII, MnII,
SiII), the accreting material appears to be enriched to about 0.4
(albeit with large uncertainties: ), which is
comparable to the galaxy metallicity (), implying a
large recycling fraction from past outflows. Blue-shifted MgII and FeII
absorptions in the galaxy spectrum from the MUSE data reveal the presence of an
outflow. The MgII and FeII doublet ratios indicate emission infilling due to
scattering processes, but the MUSE data do not show any signs of fluorescent
FeII* emission.Comment: 17 pages, 11 figures, in press (ApJ), minor edits after the proofs.
Data available at http://muse-vlt.eu/science/j1422
Acoustic Phonon-Assisted Resonant Tunneling via Single Impurities
We perform the investigations of the resonant tunneling via impurities
embedded in the AlAs barrier of a single GaAs/AlGaAs heterostructure. In the
characteristics measured at 30mK, the contribution of individual donors
is resolved and the fingerprints of phonon assistance in the tunneling process
are seen. The latter is confirmed by detailed analysis of the tunneling rates
and the modeling of the resonant tunneling contribution to the current.
Moreover, fluctuations of the local structure of the DOS (LDOS) and Fermi edge
singularities are observed.Comment: accepted in Phys. Rev.
A class of nonlinear wave equations containing the continuous Toda case
We consider a nonlinear field equation which can be derived from a binomial
lattice as a continuous limit. This equation, containing a perturbative
friction-like term and a free parameter , reproduces the Toda case (in
absence of the friction-like term) and other equations of physical interest, by
choosing particular values of . We apply the symmetry and the
approximate symmetry approach, and the prolongation technique. Our main purpose
is to check the limits of validity of different analytical methods in the study
of nonlinear field equations. We show that the equation under investigation
with the friction-like term is characterized by a finite-dimensional Lie
algebra admitting a realization in terms of boson annhilation and creation
operators. In absence of the friction-like term, the equation is linearized and
connected with equations of the Bessel type. Examples of exact solutions are
displayed, and the algebraic structure of the equation is discussed.Comment: Latex file + [equations.sty], 22 p
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