263 research outputs found
Volumes of polytopes in spaces of constant curvature
We overview the volume calculations for polyhedra in Euclidean, spherical and
hyperbolic spaces. We prove the Sforza formula for the volume of an arbitrary
tetrahedron in and . We also present some results, which provide a
solution for Seidel problem on the volume of non-Euclidean tetrahedron.
Finally, we consider a convex hyperbolic quadrilateral inscribed in a circle,
horocycle or one branch of equidistant curve. This is a natural hyperbolic
analog of the cyclic quadrilateral in the Euclidean plane. We find a few
versions of the Brahmagupta formula for the area of such quadrilateral. We also
present a formula for the area of a hyperbolic trapezoid.Comment: 22 pages, 9 figures, 58 reference
Demonstration of the temporal matter-wave Talbot effect for trapped matter waves
We demonstrate the temporal Talbot effect for trapped matter waves using
ultracold atoms in an optical lattice. We investigate the phase evolution of an
array of essentially non-interacting matter waves and observe matter-wave
collapse and revival in the form of a Talbot interference pattern. By using
long expansion times, we image momentum space with sub-recoil resolution,
allowing us to observe fractional Talbot fringes up to 10th order.Comment: 17 pages, 7 figure
Kaon Production and Kaon to Pion Ratio in Au+Au Collisions at \snn=130 GeV
Mid-rapidity transverse mass spectra and multiplicity densities of charged
and neutral kaons are reported for Au+Au collisions at \snn=130 GeV at RHIC.
The spectra are exponential in transverse mass, with an inverse slope of about
280 MeV in central collisions. The multiplicity densities for these particles
scale with the negative hadron pseudo-rapidity density. The charged kaon to
pion ratios are and
for the most central collisions. The ratio is lower than the same
ratio observed at the SPS while the is higher than the SPS result.
Both ratios are enhanced by about 50% relative to p+p and +p
collision data at similar energies.Comment: 6 pages, 3 figures, 1 tabl
The energy dependence of angular correlations inferred from mean- fluctuation scale dependence in heavy ion collisions at the SPS and RHIC
We present the first study of the energy dependence of angular
correlations inferred from event-wise mean transverse momentum
fluctuations in heavy ion collisions. We compare our large-acceptance
measurements at CM energies $\sqrt{s_{NN}} =$ 19.6, 62.4, 130 and 200 GeV to
SPS measurements at 12.3 and 17.3 GeV. $p_t$ angular correlation structure
suggests that the principal source of $p_t$ correlations and fluctuations is
minijets (minimum-bias parton fragments). We observe a dramatic increase in
correlations and fluctuations from SPS to RHIC energies, increasing linearly
with $\ln \sqrt{s_{NN}}$ from the onset of observable jet-related
fluctuations near 10 GeV.Comment: 10 pages, 4 figure
Phi meson production in Au+Au and p+p collisions at sqrt (s)=200 GeV
We report the STAR measurement of Phi meson production in Au+Au and p+p
collisions at sqrt (s)=200 GeV. Using the event mixing technique, the Phi
spectra and yields are obtained at mid-rapidity for five centrality bins in
Au+Au collisions and for non-singly-diffractive p+p collisions. It is found
that the Phi transverse momentum distributions from Au+Au collisions are better
fitted with a single-exponential while the p+p spectrum is better described by
a double-exponential distribution. The measured nuclear modification factors
indicate that Phi production in central Au+Au collisions is suppressed relative
to peripheral collisions when scaled by the number of binary collisions. The
systematics of versus centrality and the constant Phi/K- ratio versus beam
species, centrality, and collision energy rule out kaon coalescence as the
dominant mechanism for Phi production.Comment: 6 pages, 3 figures, submitted to Phys. Rev. Let
Azimuthal anisotropy at RHIC: the first and fourth harmonics
We report the first observations of the first harmonic (directed flow, v_1),
and the fourth harmonic (v_4), in the azimuthal distribution of particles with
respect to the reaction plane in Au+Au collisions at the Relativistic Heavy Ion
Collider (RHIC). Both measurements were done taking advantage of the large
elliptic flow (v_2) generated at RHIC. From the correlation of v_2 with v_1 it
is determined that v_2 is positive, or {\it in-plane}. The integrated v_4 is
about a factor of 10 smaller than v_2. For the sixth (v_6) and eighth (v_8)
harmonics upper limits on the magnitudes are reported.Comment: 6 pages with 3 figures, as accepted for Phys. Rev. Letters The data
tables are at
http://www.star.bnl.gov/central/publications/pubDetail.php?id=3
Pion, kaon, proton and anti-proton transverse momentum distributions from p+p and d+Au collisions at GeV
Identified mid-rapidity particle spectra of , , and
from 200 GeV p+p and d+Au collisions are reported. A
time-of-flight detector based on multi-gap resistive plate chamber technology
is used for particle identification. The particle-species dependence of the
Cronin effect is observed to be significantly smaller than that at lower
energies. The ratio of the nuclear modification factor () between
protons and charged hadrons () in the transverse momentum
range GeV/c is measured to be
(stat)(syst) in minimum-bias collisions and shows little
centrality dependence. The yield ratio of in minimum-bias d+Au
collisions is found to be a factor of 2 lower than that in Au+Au collisions,
indicating that the Cronin effect alone is not enough to account for the
relative baryon enhancement observed in heavy ion collisions at RHIC.Comment: 6 pages, 4 figures, 1 table. We extended the pion spectra from
transverse momentum 1.8 GeV/c to 3. GeV/
Experimental and Theoretical Challenges in the Search for the Quark Gluon Plasma: The STAR Collaboration's Critical Assessment of the Evidence from RHIC Collisions
We review the most important experimental results from the first three years
of nucleus-nucleus collision studies at RHIC, with emphasis on results from the
STAR experiment, and we assess their interpretation and comparison to theory.
The theory-experiment comparison suggests that central Au+Au collisions at RHIC
produce dense, rapidly thermalizing matter characterized by: (1) initial energy
densities above the critical values predicted by lattice QCD for establishment
of a Quark-Gluon Plasma (QGP); (2) nearly ideal fluid flow, marked by
constituent interactions of very short mean free path, established most
probably at a stage preceding hadron formation; and (3) opacity to jets. Many
of the observations are consistent with models incorporating QGP formation in
the early collision stages, and have not found ready explanation in a hadronic
framework. However, the measurements themselves do not yet establish
unequivocal evidence for a transition to this new form of matter. The
theoretical treatment of the collision evolution, despite impressive successes,
invokes a suite of distinct models, degrees of freedom and assumptions of as
yet unknown quantitative consequence. We pose a set of important open
questions, and suggest additional measurements, at least some of which should
be addressed in order to establish a compelling basis to conclude definitively
that thermalized, deconfined quark-gluon matter has been produced at RHIC.Comment: 101 pages, 37 figures; revised version to Nucl. Phys.
Strange anti-particle to particle ratios at mid-rapidity in sqrt(s_NN)= 130 GeV Au+Au Collisions
Values of the ratios in the mid-rapidity yields of anti-Lambda/Lambda = 0.71
+/- 0.01(stat.) +/- 0.04(sys.), anti-Xi+/Xi- = 0.83 +/- 0.04(stat.) +/- 0.05
(sys.), anti-Omega+/Omega- = 0.95 +/- 0.15(stat) +/- 0.05(sys.) and K+/K- 1.092
+/- 0.023(combined) were obtained in central sqrt(s_NN) = 130 GeV Au+Au
collisions using the STAR detector. The ratios indicate that a fraction of the
net-baryon number from the initial system is present in the excess of hyperons
over anti-hyperons at mid-rapidity. The trend in the progression of the baryon
ratios, with increasing strange quark content, is similar to that observed in
heavy-ion collisions at lower energies. The value of these ratios may be
related to the charged kaon ratio in the framework of simple quark-counting and
thermal models.Comment: 6 pages, 3 figures, revtex4, now accepted by Physics Letters B. All
figures improved for clarity, fig. 2 now has kaon ratio separated by
technique, fig. 3 now has additional other RHIC data points. Minor
clarifications in text in response to referee comments. Updated ref
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