5,913 research outputs found
New coins from old, smoothly
Given a (known) function , we consider the problem of
simulating a coin with probability of heads by tossing a coin with
unknown heads probability , as well as a fair coin, times each, where
may be random. The work of Keane and O'Brien (1994) implies that such a
simulation scheme with the probability equal to 1 exists iff
is continuous. Nacu and Peres (2005) proved that is real analytic in an
open set iff such a simulation scheme exists with the
probability decaying exponentially in for every . We
prove that for non-integer, is in the space if
and only if a simulation scheme as above exists with , where \Delta_n(x)\eqbd \max \{\sqrt{x(1-x)/n},1/n \}.
The key to the proof is a new result in approximation theory:
Let \B_n be the cone of univariate polynomials with nonnegative Bernstein
coefficients of degree . We show that a function is in
if and only if has a series representation
with F_n \in \B_n and for all and . We also provide a
counterexample to a theorem stated without proof by Lorentz (1963), who claimed
that if some \phi_n \in \B_n satisfy for all and , then .Comment: 29 pages; final version; to appear in Constructive Approximatio
Nature of the quantum phase transitions in the two-dimensional hardcore boson model
We use two Quantum Monte Carlo algorithms to map out the phase diagram of the
two-dimensional hardcore boson Hubbard model with near () and next near
() neighbor repulsion. At half filling we find three phases: Superfluid
(SF), checkerboard solid and striped solid depending on the relative values of
, and the kinetic energy. Doping away from half filling, the
checkerboard solid undergoes phase separation: The superfluid and solid phases
co-exist but not as a single thermodynamic phase. As a function of doping, the
transition from the checkerboard solid is therefore first order. In contrast,
doping the striped solid away from half filling instead produces a striped
supersolid phase: Co-existence of density order with superfluidity as a single
phase. One surprising result is that the entire line of transitions between the
SF and checkerboard solid phases at half filling appears to exhibit dynamical
O(3) symmetry restoration. The transitions appear to be in the same
universality class as the special Heisenberg point even though this symmetry is
explicitly broken by the interaction.Comment: 10 pages, 14 eps figures, include
Kinetic Turbulence
The weak collisionality typical of turbulence in many diffuse astrophysical
plasmas invalidates an MHD description of the turbulent dynamics, motivating
the development of a more comprehensive theory of kinetic turbulence. In
particular, a kinetic approach is essential for the investigation of the
physical mechanisms responsible for the dissipation of astrophysical turbulence
and the resulting heating of the plasma. This chapter reviews the limitations
of MHD turbulence theory and explains how kinetic considerations may be
incorporated to obtain a kinetic theory for astrophysical plasma turbulence.
Key questions about the nature of kinetic turbulence that drive current
research efforts are identified. A comprehensive model of the kinetic turbulent
cascade is presented, with a detailed discussion of each component of the model
and a review of supporting and conflicting theoretical, numerical, and
observational evidence.Comment: 31 pages, 3 figures, 99 references, Chapter 6 in A. Lazarian et al.
(eds.), Magnetic Fields in Diffuse Media, Astrophysics and Space Science
Library 407, Springer-Verlag Berlin Heidelberg (2015
Evidence for a Binary Companion to the Central Compact Object 1E 1207.4-5209
Unique among neutron stars, 1E 1207.4-5209 is an X-ray pulsar with a spin
period of 424 ms that contains at least two strong absorption features in its
energy spectrum. This neutron star has been identified as a member of the
radio-quiet compact central objects in supernova remnants. It has been found
that 1E 1207.4-5209 is not spinning down monotonically suggesting that this
neutron star undergoes strong, frequent glitches, contains a fall-back disk, or
possess a binary companion. Here, we report on a sequence of seven XMM-Newton
observations of 1E 1207.4-5209 performed during a 40 day window in June/July
2005. Due to unanticipated variance in the phase measurements beyond the
statistical uncertainties, we could not identify a unique phase-coherent timing
solution. The three most probable timing solutions give frequency time
derivatives of +0.9, -2.6, and +1.6 X 10^(-12) Hz/s (listed in descending order
of significance). We conclude that the local frequency derivative during our
XMM-Newton observing campaign differs from the long-term spin-down rate by more
than an order of magnitude, effectively ruling out glitch models for 1E
1207.4-5209. If the long-term spin frequency variations are caused by timing
noise, the strength of the timing noise in 1E 1207.4-5209 is much stronger than
in other pulsars with similar period derivatives. Therefore, it is highly
unlikely that the spin variations are caused by the same physical process that
causes timing noise in other isolated pulsars. The most plausible scenario for
the observed spin irregularities is the presence of a binary companion to 1E
1207.4-5209. We identified a family of orbital solutions that are consistent
with our phase-connected timing solution, archival frequency measurements, and
constraints on the companions mass imposed by deep IR and optical observations.Comment: 8 pages, 4 figures. To be published in the proceedings of "Isolated
Neutron Stars: from the Interior to the Surface" (April 24-28, 2006) - eds.
D. Page, R. Turolla & S. Zan
Production of massive stable particles in inflaton decay
We point out that inflaton decays can be a copious source of stable or
long--lived particles with mass exceeding the reheat temperature .
Once higher order processes are included, this statement is true for any
particle with renormalizable (gauge or Yukawa) interactions. This contribution
to the density often exceeds the contribution from thermal
production, leading to significantly stronger constraints on model parameters
than those resulting from thermal production alone. For example, we all
but exclude models containing stable charged particles with mass less than half
the mass of the inflaton.Comment: 4 revtex pages, 1 figure (uses axodraw). Slightly modified for better
clarification, few changes in references. Final verssion published in Phys.
Rev. Let
Astrophysical Axion Bounds
Axion emission by hot and dense plasmas is a new energy-loss channel for
stars. Observational consequences include a modification of the solar
sound-speed profile, an increase of the solar neutrino flux, a reduction of the
helium-burning lifetime of globular-cluster stars, accelerated white-dwarf
cooling, and a reduction of the supernova SN 1987A neutrino burst duration. We
review and update these arguments and summarize the resulting axion
constraints.Comment: Contribution to Axion volume of Lecture Notes in Physics, 20 pages, 3
figure
3-d Lattice QCD Free Energy to Four Loops
We compute the expansion of the 3-d Lattice QCD free energy to four loop
order by means of Numerical Stochastic Perturbation Theory. The first and
second order are already known and are correctly reproduced. The third and
fourth order coefficients are new results. The known logarithmic divergence in
the fourth order is correctly identified. We comment on the relevance of our
computation in the context of dimensionally reduced finite temperature QCD.Comment: 8 pages, 3 figures, latex typeset with JHEP3.cl
Axion and neutrino physics from anomaly cancellation
It has been recently shown that the requirement of anomaly cancellation in a
(non-supersymmetric) six-dimensional version of the standard model fixes the
field content to the known three generations. We discuss the phenomenological
consequences of the cancellation of the local anomalies: the strong CP problem
is solved and the fundamental scale of the theory is bounded by the physics of
the axion. Neutrinos acquire a mass in the range suggested by atmospheric
experiments.Comment: 9 pages, RevTeX
The second US Naval Observatory CCD Astrograph Catalog (UCAC2)
The second USNO CCD Astrograph Catalog, UCAC2 was released in July 2003.
Positions and proper motions for 48,330,571 sources (mostly stars) are
available on 3 CDs, supplemented with 2MASS photometry for 99.5% of the
sources. The catalog covers the sky area from -90 to +40 degrees declination,
going up to +52 in some areas; this completely supersedes the UCAC1 released in
2001. Current epoch positions are obtained from observations with the USNO
8-inch Twin Astrograph equipped with a 4k CCD camera. The precision of the
positions are 15 to 70 mas, depending on magnitude, with estimated systematic
errors of 10 mas or below. Proper motions are derived by utilizing over 140
ground-and space-based catalogs, including Hipparcos/Tycho, the AC2000.2, as
well as yet unpublished re-measures of the AGK2 plates and scans from the NPM
and SPM plates. Proper motion errors are about 1 to 3 mas/yr for stars to 12th
magnitude, and about 4 to 7 mas/yr for fainter stars to 16th magnitude. The
observational data, astrometric reductions, results, and important information
for the users of this catalog are presented.Comment: accepted by AJ, AAS LaTeX, 14 figures, 10 table
On Epstein's trajectory model of non-relativistic quantum mechanics
In 1952 Bohm presented a theory about non-relativistic point-particles moving
along deterministic trajectories and showed how it reproduces the predictions
of standard quantum theory. This theory was actually presented before by de
Broglie in 1926, but Bohm's particular formulation of the theory inspired
Epstein to come up with a different trajectory model. The aim of this paper is
to examine the empirical predictions of this model. It is found that the
trajectories in this model are in general very different from those in the de
Broglie-Bohm theory. In certain cases they even seem bizarre and rather
unphysical. Nevertheless, it is argued that the model seems to reproduce the
predictions of standard quantum theory (just as the de Broglie-Bohm theory).Comment: 12 pages, no figures, LaTex; v2 minor improvement
- …