1,175 research outputs found
The spin contribution to the form factor of quantum graphs
Following the quantisation of a graph with the Dirac operator (spin-1/2) we
explain how additional weights in the spectral form factor K(\tau) due to spin
propagation around orbits produce higher order terms in the small-\tau
asymptotics in agreement with symplectic random matrix ensembles. We determine
conditions on the group of spin rotations sufficient to generate CSE
statistics.Comment: 9 page
Spectral Statistics for the Dirac Operator on Graphs
We determine conditions for the quantisation of graphs using the Dirac
operator for both two and four component spinors. According to the
Bohigas-Giannoni-Schmit conjecture for such systems with time-reversal symmetry
the energy level statistics are expected, in the semiclassical limit, to
correspond to those of random matrices from the Gaussian symplectic ensemble.
This is confirmed by numerical investigation. The scattering matrix used to
formulate the quantisation condition is found to be independent of the type of
spinor. We derive an exact trace formula for the spectrum and use this to
investigate the form factor in the diagonal approximation
Semiclassical Approach to Parametric Spectral Correlation with Spin 1/2
The spectral correlation of a chaotic system with spin 1/2 is universally
described by the GSE (Gaussian Symplectic Ensemble) of random matrices in the
semiclassical limit. In semiclassical theory, the spectral form factor is
expressed in terms of the periodic orbits and the spin state is simulated by
the uniform distribution on a sphere. In this paper, instead of the uniform
distribution, we introduce Brownian motion on a sphere to yield the parametric
motion of the energy levels. As a result, the small time expansion of the form
factor is obtained and found to be in agreement with the prediction of
parametric random matrices in the transition within the GSE universality class.
Moreover, by starting the Brownian motion from a point distribution on the
sphere, we gradually increase the effect of the spin and calculate the form
factor describing the transition from the GOE (Gaussian Orthogonal Ensemble)
class to the GSE class.Comment: 25 pages, 2 figure
Photometry of the Globular Cluster NGC 5466: Red Giants and Blue Stragglers
We present wide-field BVI photometry for about 11,500 stars in the
low-metallicity cluster NGC 5466. We have detected the red giant branch bump
for the first time, although it is at least 0.2 mag fainter than expected
relative to the turnoff. The number of red giants (relative to main sequence
turnoff stars) is in excellent agreement with stellar models from the
Yonsei-Yale and Teramo groups, and slightly high compared to Victoria-Regina
models. This adds to evidence that an abnormally large ratio of red giant to
main-sequence stars is not correlated with cluster metallicity. We discuss
theoretical predictions from different research groups and find that the
inclusion or exclusion of helium diffusion and strong limit Coulomb
interactions may be partly responsible.
We also examine indicators of dynamical history: the mass function exponent
and the blue straggler frequency. NGC 5466 has a very shallow mass function,
consistent with large mass loss and recently-discovered tidal tails. The blue
straggler sample is significantly more centrally concentrated than the HB or
RGB stars. We see no evidence of an upturn in the blue straggler frequency at
large distances from the center. Dynamical friction timescales indicate that
the stragglers should be more concentrated if the cluster's present density
structure has existed for most of its history. NGC 5466 also has an unusually
low central density compared to clusters of similar luminosity. In spite of
this, the specific frequency of blue stragglers that puts it right on the
frequency -- cluster M_V relation observed for other clusters.Comment: 51 pages, 21 figures, 1 electronic table, accepted to Ap
Proposal for a standard problem for micromagnetic simulations including spin-transfer torque
The spin-transfer torque between itinerant electrons and the magnetization in a ferromagnet is of fundamental interest for the applied physics community. To investigate the spin-transfer torque, powerful simulation tools are mandatory. We propose a micromagnetic standard problem includingthe spin-transfer torque that can be used for the validation and falsication of micromagnetic simulation tools. The work is based on the micromagnetic model extended by the spin-transfer torque in continuously varying magnetizations as proposed by Zhang and Li. The standard problem geometry is a permalloy cuboid of 100 nm edge length and 10 nm thickness, which contains a Landau pattern with a vortex in the center of the structure. A spin-polarized dc current density of 1012 A/m2 flows laterally through the cuboid and moves the vortex core to a new steady-state position. We show that the new vortex-core position is a sensitive measure for the correctness of micromagnetic simulatorsthat include the spin-transfer torque. The suitability of the proposed problem as a standard problem is tested by numerical results from four different finite-difference and finite-element-based simulation tools
Beyond the Heisenberg time: Semiclassical treatment of spectral correlations in chaotic systems with spin 1/2
The two-point correlation function of chaotic systems with spin 1/2 is
evaluated using periodic orbits. The spectral form factor for all times thus
becomes accessible. Equivalence with the predictions of random matrix theory
for the Gaussian symplectic ensemble is demonstrated. A duality between the
underlying generating functions of the orthogonal and symplectic symmetry
classes is semiclassically established
Systematic NLTE study of the -2.6 < [Fe/H] < 0.2 F and G dwarfs in the solar neighbourhood. I. Stellar atmosphere parameters
We present atmospheric parameters for 51 nearby FG dwarfs uniformly
distributed over the -2.60 < [Fe/H] < +0.20 metallicity range that is suitable
for the Galactic chemical evolution research. Lines of iron, Fe I and Fe II,
were used to derive a homogeneous set of effective temperatures, surface
gravities, iron abundances, and microturbulence velocities. We used
high-resolution (R>60000) Shane/Hamilton and CFHT/ESPaDOnS observed spectra and
non-local thermodynamic equilibrium (NLTE) line formation for Fe I and Fe II in
the classical 1D model atmospheres. The spectroscopic method was tested with
the 20 benchmark stars, for which there are multiple measurements of the
infrared flux method (IRFM) Teff and their Hipparcos parallax error is < 10%.
We found NLTE abundances from lines of Fe I and Fe II to be consistent within
0.06 dex for every benchmark star, when applying a scaling factor of S_H = 0.5
to the Drawinian rates of inelastic Fe+H collisions. The obtained atmospheric
parameters were checked for each program star by comparing its position in the
log g-Teff plane with the theoretical evolutionary track in the Yi et al.
(2004) grid. Our final effective temperatures lie in between the T_IRFM scales
of Alonso et al. (1996) and Casagrande et al. (2011), with a mean difference of
+46 K and -51 K, respectively. NLTE leads to higher surface gravity compared
with that for LTE. The shift in log g is smaller than 0.1 dex for stars with
either [Fe/H] > -0.75, or Teff 4.20. NLTE analysis is
crucial for the VMP turn-off and subgiant stars, for which the shift in log g
between NLTE and LTE can be up to 0.5 dex. The obtained atmospheric parameters
will be used in the forthcoming papers to determine NLTE abundances of
important astrophysical elements from lithium to europium and to improve
observational constraints on the chemo-dynamical models of the Galaxy
evolution.Comment: 18 pages, 14 figures, accepted for publication in Ap
Level spacings and periodic orbits
Starting from a semiclassical quantization condition based on the trace
formula, we derive a periodic-orbit formula for the distribution of spacings of
eigenvalues with k intermediate levels. Numerical tests verify the validity of
this representation for the nearest-neighbor level spacing (k=0). In a second
part, we present an asymptotic evaluation for large spacings, where consistency
with random matrix theory is achieved for large k. We also discuss the relation
with the method of Bogomolny and Keating [Phys. Rev. Lett. 77 (1996) 1472] for
two-point correlations.Comment: 4 pages, 2 figures; major revisions in the second part, range of
validity of asymptotic evaluation clarifie
Two-point correlations of the Gaussian symplectic ensemble from periodic orbits
We determine the asymptotics of the two-point correlation function for
quantum systems with half-integer spin which show chaotic behaviour in the
classical limit using a method introduced by Bogomolny and Keating [Phys. Rev.
Lett. 77 (1996) 1472-1475]. For time-reversal invariant systems we obtain the
leading terms of the two-point correlation function of the Gaussian symplectic
ensemble. Special attention has to be paid to the role of Kramers' degeneracy.Comment: 7 pages, no figure
Th Ages for Metal-Poor Stars
With a sample of 22 metal-poor stars, we demonstrate that the heavy element
abundance pattern (Z > 55) is the same as the r-process contributions to the
solar nebula. This bolsters the results of previous studies that there is a
universal r-process production pattern. We use the abundance of thorium in five
metal-poor stars, along with an estimate of the initial Th abundance based on
the abundances of stable r-process elements, to measure their ages. We have
four field red giants with errors of 4.2 Gyr in their ages and one M92 giant
with an error of 5.6 Gyr, based on considering the sources of observational
error only. We obtain an average age of 11.4 Gyr, which depends critically on
the assumption of an initial production ratio of Th/Eu of 0.496. If the
Universe is 15 Gyr old, then the initial Th/Eu value should be 0.590, in
agreement with some theoretical models of the r-process.Comment: 26 pages, to be published in Ap
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