On the relationship between sigma models and spin chains

We consider the two-dimensional $\rm O(3)$ non-linear sigma model with topological term using a lattice regularization introduced by Shankar and Read [Nucl.Phys. B336 (1990), 457], that is suitable for studying the strong coupling regime. When this lattice model is quantized, the coefficient $\theta$ of the topological term is quantized as $\theta=2\pi s$, with $s$ integer or half-integer. We study in detail the relationship between the low energy behaviour of this theory and the one-dimensional spin-$s$ Heisenberg model. We generalize the analysis to sigma models with other symmetries.Comment: To appear in Int. J. MOd. Phys.

The ππ→πγ⋆\pi\pi\to\pi\gamma^\star amplitude and the resonant ρ→πγ⋆\rho\to\pi\gamma^\star transition from lattice QCD

We present a determination of the $P$-wave $\pi\pi\to\pi\gamma^\star$ transition amplitude from lattice quantum chromodynamics. Matrix elements of the vector current in a finite-volume are extracted from three-point correlation functions, and from these we determine the infinite-volume amplitude using a generalization of the Lellouch-L\"uscher formalism. We determine the amplitude for a range of discrete values of the $\pi\pi$ energy and virtuality of the photon, and observe the expected dynamical enhancement due to the $\rho$ resonance. Describing the energy dependence of the amplitude, we are able to analytically continue into the complex energy plane and from the residue at the $\rho$ pole extract the $\rho\to \pi \gamma^\star$ transition form factor. This calculation, at $m_\pi\approx 400$ MeV, is the first to determine the form factor of an unstable hadron within a first principles approach to QCD.Comment: 20 pages, 16 figures, 3 table

Elaborate visual and acoustic signals evolve independently in a large, phenotypically diverse radiation of songbirds

The concept of a macroevolutionary trade-off among sexual signals has a storied history in evolutionary biology. Theory predicts that if multiple sexual signals are costly for males to produce or maintain and females prefer a single, sexually selected trait, then an inverse correlation between sexual signal elaborations is expected among species. However, empirical evidence for what has been termed the \u27transfer hypothesis\u27 is mixed, which may reflect different selective pressures among lineages, evolutionary covariates or methodological differences among studies. Here,we examine interspecific correlations between song and plumage elaboration in a phenotypically diverse, widespread radiation of songbirds, the tanagers. The tanagers (Thraupidae) are the largest family of songbirds, representing nearly 10% of all songbirds. We assess variation in song and plumage elaboration across 301 species, representing the largest scale comparative study of multimodal sexual signalling to date. We consider whether evolutionary covariates, including habitat, structural and carotenoid-based coloration, and subfamily groupings influence the relationship between song and plumage elaboration. We find that song and plumage elaboration are uncorrelated when considering all tanagers, although the relationship between song and plumage complexity varies among subfamilies. Taken together, we find that elaborate visual and vocal sexual signals evolve independently among tanagers. © 2014 The Authors Published by the Royal Society. All rights reserved

Investigating the origin of cyclical wind variability in hot, massive stars - I. On the dipolar magnetic field hypothesis

OB stars exhibit various types of spectral variability associated with wind structures, including the apparently ubiquitous discrete absorption components (DACs). These are proposed to be caused by either magnetic fields or non-radial pulsations (NRPs). In this paper, we evaluate the possible relation between large-scale, dipolar magnetic fields and the DAC phenomenon by investigating the magnetic properties of a sample of 13 OB stars exhibiting well-documented DAC behaviour. Using high-precision spectropolarimetric data acquired in part in the context of the Magnetism in Massive Stars (MiMeS) project, we find no evidence for surface dipolar magnetic fields in any of these stars. Using Bayesian inference, we compute upper limits on the strengths of the fields and use these limits to assess two potential mechanisms by which the field may influence wind outflow: magnetic wind confinement and local photospheric brightness enhancements. Within the limits we derive, both mechanisms fail to provide a systematic process capable of producing DACs in all of the stars of our sample. Therefore, this implies that dipolar fields are highly unlikely to be responsible for these structures in all massive stars, meaning that some other mechanism must come into play.Comment: 17 pages, 6 figures, accepted for publication in MNRA

Searching for Weak or Complex Magnetic Fields in Polarized Spectra of Rigel

Seventy-eight high-resolution Stokes V, Q and U spectra of the B8Iae supergiant Rigel were obtained with the ESPaDOnS spectropolarimeter at CFHT and its clone NARVAL at TBL in the context of the Magnetism in Massive Stars (MiMeS) Large Program, in order to scrutinize this core-collapse supernova progenitor for evidence of weak and/or complex magnetic fields. In this paper we describe the reduction and analysis of the data, the constraints obtained on any photospheric magnetic field, and the variability of photospheric and wind lines.Comment: IAUS272 - Active OB Stars: Structure, Evolution, Mass Loss and Critical Limit

MOBSTER – III. HD 62658: a magnetic Bp star in an eclipsing binary with a non-magnetic ‘identical twin’

HD 62658 (B9p V) is a little-studied chemically peculiar star. Light curves obtained by the Kilodegree Extremely Little Telescope (KELT) and Transiting Exoplanet Survey Satellite (TESS) show clear eclipses with a period of about 4.75 d, as well as out-of-eclipse brightness modulation with the same 4.75 d period, consistent with synchronized rotational modulation of surface chemical spots. High-resolution ESPaDOnS circular spectropolarimetry shows a clear Zeeman signature in the line profile of the primary; there is no indication of a magnetic field in the secondary. PHOEBE modelling of the light curve and radial velocities indicates that the two components have almost identical masses of about 3 M_⊙. The primary’s longitudinal magnetic field〈B_z〉 varies between about +100 and −250 G, suggesting a surface magnetic dipole strength B_d = 850 G. Bayesian analysis of the Stokes V profiles indicates B_d = 650 G for the primary and B_d < 110 G for the secondary. The primary’s line profiles are highly variable, consistent with the hypothesis that the out-of-eclipse brightness modulation is a consequence of rotational modulation of that star’s chemical spots. We also detect a residual signal in the light curve after removal of the orbital and rotational modulations, which might be pulsational in origin; this could be consistent with the weak line profile variability of the secondary. This system represents an excellent opportunity to examine the consequences of magnetic fields for stellar structure via comparison of two stars that are essentially identical with the exception that one is magnetic. The existence of such a system furthermore suggests that purely environmental explanations for the origin of fossil magnetic fields are incomplete

Electrical Conductivity of Fermi Liquids. I. Many-body Effect on the Drude Weight

On the basis of the Fermi liquid theory, we investigate the many-body effect on the Drude weight. In a lattice system, the Drude weight $D$ is modified by electron-electron interaction due to Umklapp processes, while it is not renormalized in a Galilean invariant system. This is explained by showing that the effective mass $m'$ for $D\propto n/m'$ is defined through the current, not velocity, of quasiparticle. It is shown that the inequality $D>0$ is required for the stability against the uniform shift of the Fermi surface. The result of perturbation theory applied for the Hubbard model indicates that $D$ as a function of the density $n$ is qualitatively modified around half filling $n\sim 1$ by Umklapp processes.Comment: 20 pages, 2 figures; J. Phys. Soc. Jpn. Vol.67, No.

Critical evaluation of magnetic field detections reported for pulsating B-type stars in the light of ESPaDOnS, Narval and reanalyzed FORS1/2 observations

Recent spectropolarimetric studies of 7 SPB and $\beta$ Cep stars have suggested that photospheric magnetic fields are more common in B-type pulsators than in the general population of B stars, suggesting a significant connection between magnetic and pulsational phenomena. We present an analysis of new and previously published spectropolarimetric observations of these stars. New Stokes $V$ observations obtained with the high-resolution ESPaDOnS and Narval instruments confirm the presence of a magnetic field in one of the stars ($\epsilon$ Lup), but find no evidence of magnetism in 5 others. A re-analysis of the published longitudinal field measurements obtained with the low-resolution FORS1/2 spectropolarimeters finds that the measurements of all stars show more scatter from zero than can be attributed to Gaussian noise, suggesting the presence of a signal and/or systematic under-estimation of error bars. Re-reduction and re-measurement of the FORS1/2 spectra from the ESO archive demonstrates that small changes in reduction procedure lead to substantial changes in the inferred longitudinal field, and substantially reduces the number of field detections at the 3$\sigma$ level. Furthermore, we find that the published periods are not unique solutions to the time series of either the original or the revised FORS1/2 data. We conclude that the reported field detections, proposed periods and field geometry models for $\alpha$ Pyx, 15 CMa, 33 Eri and V1449 Aql are artefacts of the data analysis and reduction procedures, and that magnetic fields at the reported strength are no more common in SPB/$\beta$ Cep stars than in the general population of B stars.Comment: 10 pages, 5 figures, accepted for publication in ApJ, 2012, typo correcte