Position, spin and orbital angular momentum of a relativistic electron

Motivated by recent interest in relativistic electron vortex states, we revisit the spin and orbital angular momentum properties of Dirac electrons. These are uniquely determined by the choice of the position operator for a relativistic electron. We overview two main approaches discussed in the literature: (i) the projection of operators onto the positive-energy subspace, which removes the zitterbewegung effects and correctly describes spin-orbit interaction effects, and (ii) the use of Newton-Wigner-Foldy-Wouthuysen operators based on the inverse Foldy-Wouthuysen transformation. We argue that the first approach [previously described in application to Dirac vortex beams in K.Y. Bliokh et al., Phys. Rev. Lett. 107, 174802 (2011)] has a more natural physical interpretation, including spin-orbit interactions and a nonsingular zero-mass limit, than the second one [S.M. Barnett, Phys. Rev. Lett. 118, 114802 (2017)].Comment: 10 pages, 1 table, to appear in Phys. Rev.

Geometric phases in 2D and 3D polarized fields: geometrical, dynamical, and topological aspects

Geometric phases are a universal concept that underpins numerous phenomena involving multi-component wave fields. These polarization-dependent phases are inherent in interference effects, spin-orbit interaction phenomena, and topological properties of vector wave fields. Geometric phases have been thoroughly studied in two-component fields, such as two-level quantum systems or paraxial optical waves. However, their description for fields with three or more components, such as generic nonparaxial optical fields routinely used in modern nano-optics, constitutes a nontrivial problem. Here we describe geometric, dynamical, and total phases calculated along a closed spatial contour in a multi-component complex field, with particular emphasis on 2D (paraxial) and 3D (nonparaxial) optical fields. We present several equivalent approaches: (i) an algebraic formalism, universal for any multi-component field; (ii) a dynamical approach using the Coriolis coupling between the spin angular momentum and reference-frame rotations; and (iii) a geometric representation, which unifies the Pancharatnam-Berry phase for the 2D polarization on the Poincar\'e sphere and the Majorana-sphere representation for the 3D polarized fields. Most importantly, we reveal close connections between geometric phases, angular-momentum properties of the field, and topological properties of polarization singularities in 2D and 3D fields, such as C-points and polarization M\"obius strips.Comment: 21 pages, 11 figures, to appear in Rep. Prog. Phy

Repurchasing Shares on a Second Trading Line

This paper studies a unique buyback method allowing firms to reacquire their own shares on a separate trading line where only the firm is allowed to buy shares. This temporary trading platform is opened concurrently with the original trading line on the stock exchange. This share repurchase method is called the Second Trading Line and has been extensively used by Swiss companies since 1997. This type of repurchase is unique for two reasons. First, unlike open market programs, the repurchasing company does not trade under the cover of anonymity. Second, all transactions made by the repurchasing firm are publicly available in real time to every market participant. This is a case of instantaneous disclosure which contrasts sharply with other markets characterized by delayed or no disclosure. Using actual repurchase data from all buybacks implemented through second trading lines, we find that managers exhibit timing ability for the majority of programs. We also document that the daily repurchase decision is statistically associated with short-term price changes. However, we reject the opportunistic repurchase hypothesis and find no evidence that managers exploit their information advantage when reacquiring shares. We also find that repurchases on the second trading line have a beneficial impact on the liquidity of repurchasing firms (i.e., higher trading volumes, smaller bid-ask spreads, and thicker total depths). Exchanges and regulators may consider the second trading line an attractive share reacquisition mechanism because of its transparency and positive liquidity effects.Share Repurchases;Disclosure Environment;Information Asymmetry;Liquidity

An Empirical Connection between the UV Color of Early Type Galaxies and the Stellar Initial Mass Function

Using new UV magnitudes for a sample of early-type galaxies, ETGs, with published stellar mass-to-light ratios, Upsilon_*, we find a correlation between UV color and Upsilon_* that is tighter than those previously identified between Upsilon_* and either the central stellar velocity dispersion, metallicity, or alpha enhancement. The sense of the correlation is that galaxies with larger Upsilon_* are bluer in the UV. We conjecture that differences in the lower mass end of the stellar initial mass function, IMF, are related to the nature of the extreme horizontal branch populations that are generally responsible for the UV flux in ETGs. If so, then UV color can be used to identify ETGs with particular IMF properties and to estimate Upsilon_*.Comment: Submitted for publication in ApJ Letter

P-wave diffusion in fluid-saturated medium

This paper considers the propagating P-waves in the fluid-saturated mediums that are categorized to fall into two distinct groups: insoluble and soluble mediums. P-waves are introduced with slowness in accordance to Snell Law and are shown to relate to the medium displacement and wave diffusion. Consequently, the results bear out that the propagating P-waves in the soluble medium share similar diffusive characteristic as of insoluble medium. Nonetheless, our study on fluid density in the mediums show that high density fluid promotes diffusive characteristic whiles low density fluid endorses non-diffusive P-wav

Inhomogeneous CuO_{6} Tilt Distribution and Charge/Spin Correlations in La_{2-x-y}Nd_{y}Sr_{x}CuO$_{4} around commensurate hole concentration

Phononic and magnetic Raman scattering are studied in La$_{2-x-y}$Nd$_{y}$Sr$_{x}$CuO$_{4}$ with three doping concentrations: x ~ 1/8, y = 0; x ~ 1/8, y = 0.4; and x = 0.01, y = 0. We observe strong disorder in the tilt pattern of the CuO_{6} octahedra in both the orthorhombic and tetragonal phases which persist down to 10 K and are coupled to bond disorder in the cation layers around 1/8 doping independent of Nd concentration. The weak magnitude of existing charge/spin modulations in the Nd doped structure does not allow us to detect the specific Raman signatures on lattice dynamics or two-magnon scattering around 2200 cm-1.Comment: to be published in Phys. Rev.