4,991 research outputs found
Attitude determination of the spin-stabilized Project Scanner spacecraft
Attitude determination of spin-stabilized spacecraft using star mapping techniqu
Fractional -scaling for quantum kicked rotors without cantori
Previous studies of quantum delta-kicked rotors have found momentum
probability distributions with a typical width (localization length )
characterized by fractional -scaling, ie in regimes
and phase-space regions close to `golden-ratio' cantori. In contrast, in
typical chaotic regimes, the scaling is integer, . Here we
consider a generic variant of the kicked rotor, the random-pair-kicked particle
(RP-KP), obtained by randomizing the phases every second kick; it has no KAM
mixed phase-space structures, like golden-ratio cantori, at all. Our unexpected
finding is that, over comparable phase-space regions, it also has fractional
scaling, but . A semiclassical analysis indicates that the
scaling here is of quantum origin and is not a signature of
classical cantori.Comment: 5 pages, 4 figures, Revtex, typos removed, further analysis added,
authors adjuste
What is the probability that a random integral quadratic form in variables has an integral zero?
We show that the density of quadratic forms in variables over that are isotropic is a rational function of , where the rational
function is independent of , and we determine this rational function
explicitly. When real quadratic forms in variables are distributed
according to the Gaussian Orthogonal Ensemble (GOE) of random matrix theory, we
determine explicitly the probability that a random such real quadratic form is
isotropic (i.e., indefinite).
As a consequence, for each , we determine an exact expression for the
probability that a random integral quadratic form in variables is isotropic
(i.e., has a nontrivial zero over ), when these integral quadratic
forms are chosen according to the GOE distribution. In particular, we find an
exact expression for the probability that a random integral quaternary
quadratic form has an integral zero; numerically, this probability is
approximately .Comment: 17 pages. This article supercedes arXiv:1311.554
Using Big Bang Nucleosynthesis to Extend CMB Probes of Neutrino Physics
We present calculations showing that upcoming Cosmic Microwave Background
(CMB) experiments will have the power to improve on current constraints on
neutrino masses and provide new limits on neutrino degeneracy parameters. The
latter could surpass those derived from Big Bang Nucleosynthesis (BBN) and the
observationally-inferred primordial helium abundance. These conclusions derive
from our Monte Carlo Markov Chain (MCMC) simulations which incorporate a full
BBN nuclear reaction network. This provides a self-consistent treatment of the
helium abundance, the baryon number, the three individual neutrino degeneracy
parameters and other cosmological parameters. Our analysis focuses on the
effects of gravitational lensing on CMB constraints on neutrino rest mass and
degeneracy parameter. We find for the PLANCK experiment that total (summed)
neutrino mass eV could be ruled out at or better.
Likewise neutrino degeneracy parameters and could be detected or ruled out at
confidence, or better. For POLARBEAR we find that the corresponding detectable
values are , , and , while for EPIC we obtain ,
, and . Our forcast for
EPIC demonstrates that CMB observations have the potential to set constraints
on neutrino degeneracy parameters which are better than BBN-derived limits and
an order of magnitude better than current WMAP-derived limits.Comment: 27 pages, 11 figures, matches published version in JCA
Engineering aspects of the selective acid leaching process for refining mixed nickel-cobalt hydroxide
The precipitation of mixed hydroxide is increasingly being considered as an intermediate step in the hydrometallurgical processing of nickel and cobalt. Producers currently receive roughly 75% of the value of the contained nickel and zero value for contained cobalt. In this paper, a new selective leach process for refining the mixed hydroxide is described that allows for recovery of the majority of the nickel as final metal product and realizes value for the cobalt. The features of the new process are compared with two other alternative routes (1) acid leaching followed by solvent extraction of the cobalt and (2) ammonia leaching followed by solvent extraction of the nickel. The outcomes of a process simulation for the selective acid leaching process are presented along with capital and operating cost estimates. The operating and capital costs of the process are estimated to ±50%. For the processing of 50,000 t-Ni/y in the form of MHP, the operating cost is estimated to be 0.87 per lb of Ni contained in MHP) and the capital cost as defined for this study is estimated to be 1.5 billion AUD. Over 94% of the total value (nickel and cobalt) contained in the MHP is extracted by the new process
Number fields and function fields:Coalescences, contrasts and emerging applications
The similarity between the density of the primes and the density of irreducible polynomials defined over a finite field of q elements was first observed by Gauss. Since then, many other analogies have been uncovered between arithmetic in number fields and in function fields defined over a finite field. Although an active area of interaction for the past half century at least, the language and techniques used in analytic number theory and in the function field setting are quite different, and this has frustrated interchanges between the two areas. This situation is currently changing, and there has been substantial progress on a number of problems stimulated by bringing together ideas from each field. We here introduce the papers published in this Theo Murphy meeting issue, where some of the recent developments are explained
On the resonance eigenstates of an open quantum baker map
We study the resonance eigenstates of a particular quantization of the open
baker map. For any admissible value of Planck's constant, the corresponding
quantum map is a subunitary matrix, and the nonzero component of its spectrum
is contained inside an annulus in the complex plane, . We consider semiclassical sequences of eigenstates, such that the
moduli of their eigenvalues converge to a fixed radius . We prove that, if
the moduli converge to , then the sequence of eigenstates
converges to a fixed phase space measure . The same holds for
sequences with eigenvalue moduli converging to , with a different
limit measure . Both these limiting measures are supported on
fractal sets, which are trapped sets of the classical dynamics. For a general
radius , we identify families of eigenstates with
precise self-similar properties.Comment: 32 pages, 2 figure
Applications and generalizations of Fisher-Hartwig asymptotics
Fisher-Hartwig asymptotics refers to the large form of a class of
Toeplitz determinants with singular generating functions. This class of
Toeplitz determinants occurs in the study of the spin-spin correlations for the
two-dimensional Ising model, and the ground state density matrix of the
impenetrable Bose gas, amongst other problems in mathematical physics. We give
a new application of the original Fisher-Hartwig formula to the asymptotic
decay of the Ising correlations above , while the study of the Bose gas
density matrix leads us to generalize the Fisher-Hartwig formula to the
asymptotic form of random matrix averages over the classical groups and the
Gaussian and Laguerre unitary matrix ensembles. Another viewpoint of our
generalizations is that they extend to Hankel determinants the Fisher-Hartwig
asymptotic form known for Toeplitz determinants.Comment: 25 page
On the moments of the moments of the characteristic polynomials of Haar distributed symplectic and orthogonal matrices
We establish formulae for the moments of the moments of the characteristic
polynomials of random orthogonal and symplectic matrices in terms of certain
lattice point count problems. This allows us to establish asymptotic formulae
when the matrix-size tends to infinity in terms of the volumes of certain
regions involving continuous Gelfand-Tsetlin patterns with constraints. The
results we find differ from those in the unitary case considered previouslyComment: 31 page
Renormalization of Quantum Anosov Maps: Reduction to Fixed Boundary Conditions
A renormalization scheme is introduced to study quantum Anosov maps (QAMs) on
a torus for general boundary conditions (BCs), whose number () is always
finite. It is shown that the quasienergy eigenvalue problem of a QAM for {\em
all} BCs is exactly equivalent to that of the renormalized QAM (with
Planck's constant ) at some {\em fixed} BCs that can
be of four types. The quantum cat maps are, up to time reversal, fixed points
of the renormalization transformation. Several results at fixed BCs, in
particular the existence of a complete basis of ``crystalline'' eigenstates in
a classical limit, can then be derived and understood in a simple and
transparent way in the general-BCs framework.Comment: REVTEX, 12 pages, 1 table. To appear in Physical Review Letter
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