New coins from old, smoothly

Given a (known) function $f:[0,1] \to (0,1)$, we consider the problem of simulating a coin with probability of heads $f(p)$ by tossing a coin with unknown heads probability $p$, as well as a fair coin, $N$ times each, where $N$ may be random. The work of Keane and O'Brien (1994) implies that such a simulation scheme with the probability $\P_p(N<\infty)$ equal to 1 exists iff $f$ is continuous. Nacu and Peres (2005) proved that $f$ is real analytic in an open set $S \subset (0,1)$ iff such a simulation scheme exists with the probability $\P_p(N>n)$ decaying exponentially in $n$ for every $p \in S$. We prove that for $\alpha>0$ non-integer, $f$ is in the space $C^\alpha [0,1]$ if and only if a simulation scheme as above exists with $\P_p(N>n) \le C (\Delta_n(p))^\alpha$, 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 $n$. We show that a function $f:[0,1] \to (0,1)$ is in $C^\alpha [0,1]$ if and only if $f$ has a series representation $\sum_{n=1}^\infty F_n$ with F_n \in \B_n and $\sum_{k>n} F_k(x) \le C(\Delta_n(x))^\alpha$ for all $x \in [0,1]$ and $n \ge 1$. 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 $|f(x)-\phi_n(x)| \le C (\Delta_n(x))^\alpha$ for all $x \in [0,1]$ and $n \ge 1$, then $f \in C^\alpha [0,1]$.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 ($V_1$) and next near ($V_2$) neighbor repulsion. At half filling we find three phases: Superfluid (SF), checkerboard solid and striped solid depending on the relative values of $V_1$, $V_2$ 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 $V_2$ 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 $\chi$ with mass exceeding the reheat temperature $T_R$. Once higher order processes are included, this statement is true for any $\chi$ particle with renormalizable (gauge or Yukawa) interactions. This contribution to the $\chi$ density often exceeds the contribution from thermal $\chi$ production, leading to significantly stronger constraints on model parameters than those resulting from thermal $\chi$ 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

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

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

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