593 research outputs found
Instabilities in the two-dimensional cubic nonlinear Schrodinger equation
The two-dimensional cubic nonlinear Schrodinger equation (NLS) can be used as
a model of phenomena in physical systems ranging from waves on deep water to
pulses in optical fibers. In this paper, we establish that every
one-dimensional traveling wave solution of NLS with trivial phase is unstable
with respect to some infinitesimal perturbation with two-dimensional structure.
If the coefficients of the linear dispersion terms have the same sign then the
only unstable perturbations have transverse wavelength longer than a
well-defined cut-off. If the coefficients of the linear dispersion terms have
opposite signs, then there is no such cut-off and as the wavelength decreases,
the maximum growth rate approaches a well-defined limit.Comment: 4 pages, 4 figure
Quantum Vacuum Instability Near Rotating Stars
We discuss the Starobinskii-Unruh process for the Kerr black hole. We show
how this effect is related to the theory of squeezed states. We then consider a
simple model for a highly relativistic rotating star and show that the
Starobinskii-Unruh effect is absent.Comment: 17 Pages, (accepted by PRD), (previously incorrect header files have
been corrected
Tracking Black Holes in Numerical Relativity
This work addresses and solves the problem of generically tracking black hole
event horizons in computational simulation of black hole interactions.
Solutions of the hyperbolic eikonal equation, solved on a curved spacetime
manifold containing black hole sources, are employed in development of a robust
tracking method capable of continuously monitoring arbitrary changes of
topology in the event horizon, as well as arbitrary numbers of gravitational
sources. The method makes use of continuous families of level set viscosity
solutions of the eikonal equation with identification of the black hole event
horizon obtained by the signature feature of discontinuity formation in the
eikonal's solution. The method is employed in the analysis of the event horizon
for the asymmetric merger in a binary black hole system. In this first such
three dimensional analysis, we establish both qualitative and quantitative
physics for the asymmetric collision; including: 1. Bounds on the topology of
the throat connecting the holes following merger, 2. Time of merger, and 3.
Continuous accounting for the surface of section areas of the black hole
sources.Comment: 14 pages, 16 figure
On the construction of a geometric invariant measuring the deviation from Kerr data
This article contains a detailed and rigorous proof of the construction of a
geometric invariant for initial data sets for the Einstein vacuum field
equations. This geometric invariant vanishes if and only if the initial data
set corresponds to data for the Kerr spacetime, and thus, it characterises this
type of data. The construction presented is valid for boosted and non-boosted
initial data sets which are, in a sense, asymptotically Schwarzschildean. As a
preliminary step to the construction of the geometric invariant, an analysis of
a characterisation of the Kerr spacetime in terms of Killing spinors is carried
out. A space spinor split of the (spacetime) Killing spinor equation is
performed, to obtain a set of three conditions ensuring the existence of a
Killing spinor of the development of the initial data set. In order to
construct the geometric invariant, we introduce the notion of approximate
Killing spinors. These spinors are symmetric valence 2 spinors intrinsic to the
initial hypersurface and satisfy a certain second order elliptic equation
---the approximate Killing spinor equation. This equation arises as the
Euler-Lagrange equation of a non-negative integral functional. This functional
constitutes part of our geometric invariant ---however, the whole functional
does not come from a variational principle. The asymptotic behaviour of
solutions to the approximate Killing spinor equation is studied and an
existence theorem is presented.Comment: 36 pages. Updated references. Technical details correcte
Focusing of geodesic congruences in an accelerated expanding Universe
We study the accelerated expansion of the Universe through its consequences
on a congruence of geodesics. We make use of the Raychaudhuri equation which
describes the evolution of the expansion rate for a congruence of timelike or
null geodesics. In particular, we focus on the space-time geometry contribution
to this equation. By straightforward calculation from the metric of a
Robertson-Walker cosmological model, it follows that in an accelerated
expanding Universe the space-time contribution to the Raychaudhuri equation is
positive for the fundamental congruence, favoring a non-focusing of the
congruence of geodesics. However, the accelerated expansion of the present
Universe does not imply a tendency of the fundamental congruence to diverge. It
is shown that this is in fact the case for certain congruences of timelike
geodesics without vorticity. Therefore, the focusing of geodesics remains
feasible in an accelerated expanding Universe. Furthermore, a negative
contribution to the Raychaudhuri equation from space-time geometry which is
usually interpreted as the manifestation of the attractive character of gravity
is restored in an accelerated expanding Robertson-Walker space-time at high
speeds.Comment: 11 pages, 2 figures. Final version changed to match published version
in JCAP. References updated. Conclusions unchange
Unusual bound states of quark matter within the NJL model
Properties of dense quark matter in and out of chemical equilibrium are
studied within the SU(3) Nambu-Jona-Lasinio model. In addition to the 4-fermion
scalar and vector terms the model includes also the 6-fermion flavour mixing
interaction. First we study a novel form of deconfined matter, meso-matter,
which is composed of equal number of quarks and antiquarks. It can be thought
of as a strongly compressed meson gas where mesons are melted into their
elementary constituents, quarks and antiquarks. Strongly bound states in this
quark-antiquark matter are predicted for all flavour combinations of
quark-antiquark pairs. The maximum binding energy reaches up to 180 MeV per
pair for mixtures with about 70% of strange quark-antiquark pairs. Equilibrated
baryon-rich quark matter with various flavour compositions is also studied. In
this case only shallow bound states appear in systems with a significant
admixture (about 40%) of strange quarks (strangelets). Their binding energies
are quite sensitive to the relative strengths of scalar and vector
interactions. The common property of all these bound states is that they appear
at high particle densities when the chiral symmetry is nearly restored. Thermal
properties of meso-matter as well as chemically equilibrated strange quark
matter are also investigated. Possible decay modes of these bound states are
discussed.Comment: 26 pages, 16 PostScript figures, RevTe
Search for CP Violation in Charged D Meson Decays
We report results of a search for CP violation in the singly
Cabibbo-suppressed decays D+ -> K- K+ pi+, phi pi+, K*(892)0 K+, and pi- pi+
pi+ based on data from the charm hadroproduction experiment E791 at Fermilab.
We search for a difference in the D+ and D- decay rates for each of the final
states. No evidence for a difference is seen. The decay rate asymmetry
parameters A(CP), defined as the difference in the D+ and D- decay rates
divided by the sum of the decay rates, are measured to be: A(CP)(K K pi) =
-0.014 +/- 0.029, A(CP)(phi pi) = -0.028 +/- 0.036, A(CP)(K*(892) K) = -0.010
+/- 0.050, and A(CP)(pi pi pi) = -0.017 +/- 0.042.Comment: 13 pages, 5 figures, 1 table; Elsevier LaTe
Specific Heat Study of the Magnetic Superconductor HoNi2B2C
The complex magnetic transitions and superconductivity of HoNi2B2C were
studied via the dependence of the heat capacity on temperature and in-plane
field angle. We provide an extended, comprehensive magnetic phase diagram for B
// [100] and B // [110] based on the thermodynamic measurements. Three magnetic
transitions and the superconducting transition were clearly observed. The 5.2 K
transition (T_{N}) shows a hysteresis with temperature, indicating the first
order nature of the transition at B=0 T. The 6 K transition (T_{M}), namely the
onset of the long-range ordering, displays a dramatic in-plane anisotropy:
T_{M} increases with increasing magnetic field for B // [100] while it
decreases with increasing field for B // [110]. The anomalous anisotropy in
T_{M} indicates that the transition is related to the a-axis spiral structure.
The 5.5 K transition (T^{*}) shows similar behavior to the 5.2 K transition,
i.e., a small in-plane anisotropy and scaling with Ising model. This last
transition is ascribed to the change from a^{*} dominant phase to c^{*}
dominant phase.Comment: 9 pages, 11 figure
Branching Fractions for D0 -> K+K- and D0 -> pi+pi-, and a Search for CP Violation in D0 Decays
Using the large hadroproduced charm sample collected in experiment E791 at
Fermilab, we have measured ratios of branching fractions for the two-body
singly-Cabibbo-suppressed charged decays of the D0:
(D0 -> KK)/(D0 -> Kpi) = 0.109 +- 0.003 +- 0.003,
(D0 -> pipi)/(D0 -> Kpi) = 0.040 +- 0.002 +- 0.003, and
(D0 -> KK)/(D0 -> pipi) = 2.75 +- 0.15 +- 0.16. We have looked for
differences in the decay rates of D0 and D0bar to the CP eigenstates K+K- and
pi+pi-, and have measured the CP asymmetry parameters
A_CP(K+K-) = -0.010 +- 0.049 +- 0.012 and
A_CP(pi+pi-) = -0.049 +- 0.078 +- 0.030, both consistent with zero.Comment: 10 Postscript pages, including 2 figures. Submitted to Phys. Lett.
Asymmetries between the production of D+ and D- mesons from 500 GeV/c pi- nucleon interactions as a function of xF and pt**2
We present asymmetries between the production of D+ and D- mesons in Fermilab
experiment E791 as a function of xF and pt**2. The data used here consist of
74,000 fully-reconstructed charmed mesons produced by a 500 GeV/c pi- beam on C
and Pt foils. The measurements are compared to results of models which predict
differences between the production of heavy-quark mesons that have a light
quark in common with the beam (leading particles) and those that do not
(non-leading particles). While the default models do not agree with our data,
we can reach agreement with one of them, PYTHIA, by making a limited number of
changes to parameters used
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