Faraday rotation: effect of magnetic field reversals

The standard formula for the rotation measure, RM, which determines the position angle, $\psi={\rm RM}\lambda^2$, due to Faraday rotation, includes contributions only from the portions of the ray path where the natural modes of the plasma are circularly polarized. In small regions of the ray path where the projection of the magnetic field on the ray path reverses sign (called QT regions) the modes are nearly linearly polarized. The neglect of QT regions in estimating RM is not well justified at frequencies below a transition frequency where mode coupling changes from strong to weak. By integrating the polarization transfer equation across a QT region in the latter limit, I estimate the additional contribution $\Delta\psi$ needed to correct this omission. In contrast with a result proposed by \cite{BB10}, $\Delta\psi$ is small and probably unobservable. I identify a new source of circular polarization, due to mode coupling in an asymmetric QT region. I also identify a new circular-polarization-dependent correction to the dispersion measure at low frequencies.Comment: 25 pages 1 figure, accepted for publication in The Astrophysical Journa

Signatures of integrability in charge and thermal transport in 1D quantum systems

Integrable and non-integrable systems have very different transport properties. In this work, we highlight these differences for specific one dimensional models of interacting lattice fermions using numerical exact diagonalization. We calculate the finite temperature adiabatic stiffness (or Drude weight) and isothermal stiffness (or ``Meissner'' stiffness) in electrical and thermal transport and also compute the complete momentum and frequency dependent dynamical conductivities $\sigma(q,\omega)$ and $\kappa(q,\omega)$. The Meissner stiffness goes to zero rapidly with system size for both integrable and non-integrable systems. The Drude weight shows signs of diffusion in the non-integrable system and ballistic behavior in the integrable system. The dynamical conductivities are also consistent with ballistic and diffusive behavior in the integrable and non-integrable systems respectively.Comment: 4 pages, 4 figure

A Stellar Audit: The Computation of Encounter Rates for 47 Tucanae and omega Centauri

Using King-Mitchie Models, we compute encounter rates between the various stellar species in the globular clusters $\omega$ Cen, and 47 Tuc. We also compute event rates for encounters between single stars and a population of primordial binaries. Using these rates, and what we have learnt from hydrodynamical simulations of encounters performed earlier, we compute the production rates of objects such as low-mass X-ray binaries (LMXBs), smothered neutron stars and blue stragglers (massive main-sequence stars). If 10\% of the stars are contained in primordial binaries, the production rate of interesting objects from encounters involving these binaries is as large as that from encounters between single stars. For example, encounters involving binaries produce a significant number of blue stragglers in both globular cluster models. The number of smothered neutron stars may exceed the number of low-mass X-ray binaries (LMXBs) by a factor of 5-20, which may help explain why millisecond pulsars are observed to outnumber LMXBs in globular clusters.Comment: uuencoded compressed postscript. The preprint is also available at http://www.ast.cam.ac.uk/preprint/PrePrint.htm

Electrodynamic modeling of strong coupling between a metasurface and intersubband transitions in quantum wells

Strong light-matter coupling has recently been demonstrated in sub-wavelength volumes by coupling engineered optical transitions in semiconductor heterostructures (e.g., quantum wells) to metasurface resonances via near fields. It has also been shown that different resonator shapes may lead to different Rabi splittings, though this has not yet been well explained. In this paper, our aim is to understand the correlation between resonator shape and Rabi splitting, and in particular determine and quantify the physical parameters that affect strong coupling by developing an equivalent circuit network model whose elements describe energy and dissipation. Because of the subwavelength dimension of each metasurface element, we resort to the quasi-static (electrostatic) description of the near-field and hence define an equivalent capacitance associated to each dipolar element of a flat metasurface, and we show that this is also able to accurately model the phenomenology involved in strong coupling between the metasurface and the intersubband transitions in quantum wells. We show that the spectral properties and stored energy of a metasurface/quantum-well system obtained using our model are in good agreement with both full-wave simulation and experimental results. We then analyze metasurfaces made of three different resonator geometries and observe that the magnitude of the Rabi splitting increases with the resonator capacitance in agreement with our theory, providing a phenomenological explanation for the resonator shape dependence of the strong coupling process.Comment: 10 pages, 10 figure

Red giant collisions in the galactic centre

We simulate collisions involving red-giant stars in the centre of our galaxy. Such encounters may explain the observed paucity of highly luminous red giants within the central 0.2pc. The masses of the missing stars are likely to be in the range 2 to 8 solar masses. Recent models of the galactic centre cluster's density and velocity distributions are used to calculate two-body collision rates. In particular we use stellar-evolution models to calculate the number of collisions a star will have during different evolutionary phases. We find that the number of two-body collisions per star is \lo 1 in the central 0.1 to 0.2 pc, depending strongly on the galactocentric radius. Using a 3D numerical hydrodynamics code (SPH) we simulate encounters involving cluster stars of various masses with 2 and 8 solar-mass red giants. The instantaneous mass loss in such collisions is rarely enough to destroy either giant. A fraction of the collisions do, however, lead to the formation of common envelope systems where the impactor and giant's core are enshrouded by the envelope of the giant. Such systems may evolve to expel the envelope, leaving a tight binary; the original giant is destroyed. The fraction of collisions that produce common envelope systems is sensitive to the local velocity dispersion and hence galactocentric radius. Using our collision-rate calculations we compute the time-scales for a giant star to suffer such a collision within the galactic centre. These time-scales are >10^{9-10}years and so are longer than the lifetimes of stars more-massive than 2 solar masses. Thus the observed paucity of luminous giants is unlikely to be due to the formation of common envelope systems as a result of two-body encounters involving giant stars.Comment: 10 pages, 11 figures, MNRAS (in press