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 constant magnetic field of xi 1 CMa: geometry or slow rotation?

We report recent observations of the sharp-lined magnetic beta Cep pulsator xi 1 CMa (= HD 46328). The longitudinal magnetic field of this star is detected consistently, but it is not observed to vary strongly, during nearly 5 years of observation. In this poster we evaluate whether the nearly constant longitudinal field is due to intrinsically slow rotation, or rather if the stellar or magnetic geometry is responsible

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

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.

Uniqueness of quantum states compatible with given measurement results

We discuss the uniqueness of quantum states compatible with given measurement results for a set of observables. For a given pure state, we consider two different types of uniqueness: (1) no other pure state is compatible with the same measurement results and (2) no other state, pure or mixed, is compatible with the same measurement results. For case (1), it was known that for a d-dimensional Hilbert space, there exists a set of 4d-5 observables that uniquely determines any pure state. We show that for case (2), 5d-7 observables suffice to uniquely determine any pure state. Thus, there is a gap between the results for (1) and (2), and we give some examples to illustrate this. Unique determination of a pure state by its reduced density matrices (RDMs), a special case of determination by observables, is also discussed. We improve the best-known bound on local dimensions in which almost all pure states are uniquely determined by their RDMs for case (2). We further discuss circumstances where (1) can imply (2). We use convexity of the numerical range of operators to show that when only two observables are measured, (1) always implies (2). More generally, if there is a compact group of symmetries of the state space which has the span of the observables measured as the set of fixed points, then (1) implies (2). We analyze the possible dimensions for the span of such observables. Our results extend naturally to the case of low-rank quantum states. © 2013 American Physical Society

Discovery Of A Magnetic Field In The Rapidly Rotating O-Type Secondary Of The Colliding-Wind Binary HD 47129 (Plaskett\u27s Star)

We report the detection of a strong, organized magnetic field in the secondary component of the massive O8III/I+O7.5V/III double-lined spectroscopic binary system HD 47129 (Plaskett\u27s star) in the context of the Magnetism in Massive Stars survey. Eight independent Stokes V observations were acquired using the Echelle SpectroPolarimetric Device for the Observations of Stars (ESPaDOnS) spectropolarimeter at the Canada-France-Hawaii Telescope and the Narval spectropolarimeter at the Telescope Bernard Lyot. Using least-squares deconvolution we obtain definite detections of signal in Stokes V in three observations. No significant signal is detected in the diagnostic null (N) spectra. The Zeeman signatures are broad and track the radial velocity of the secondary component; we therefore conclude that the rapidly rotating secondary component is the magnetized star. Correcting the polarized spectra for the line and continuum of the (sharp-lined) primary, we measured the longitudinal magnetic field from each observation. The longitudinal field of the secondary is variable and exhibits extreme values of -810 +/- 150 and +680 +/- 190 G, implying a minimum surface dipole polar strength of 2850 +/- 500 G. In contrast, we derive an upper limit (3 sigma) to the primary\u27s surface magnetic field of 230 G. The combination of a strong magnetic field and rapid rotation leads us to conclude that the secondary hosts a centrifugal magnetosphere fed through a magnetically confined wind. We revisit the properties of the optical line profiles and X-ray emission - previously interpreted as a consequence of colliding stellar winds - in this context. We conclude that HD 47129 represents a heretofore unique stellar system - a close, massive binary with a rapidly rotating, magnetized component - that will be a rich target for further study

The Reliability and Validity of Ankle Inversion and Eversion Torque Measurements From the Kin Com II Isokinetic Dynamometer

This study examined the test—retest reliability of a prototype device used to measure ankle inversion and eversion isokinetic average torque values. The purpose of this paper was to illustrate a situation where common isokinetic measures were reliable but not valid. Coneentric and eccentric average torque was assessed at 90 deg/s on the Kin Com II dynamometer using 14 healthy subjects in two sessions; a manufactured prototype ankle inversion/eversion attachment device was used. Reliability was assessed by performing separate intraclass correlations (ICC 2,1) on the results. The data indicated that the average torque calculated from the clockwise direction was consistently higher than those values from the counterclockwise direction, regardless of ankle movement or side measured. The validity of this prototype device to accurately measure average torque for these two ankle motions is questionable. This finding demonstrates a situation where the measures appear to be reliable while the validity of the device used to obtain the measures is suspect