Geometric Prequantization of the Moduli Space of the Vortex equations on a Riemann surface

The moduli space of solutions to the vortex equations on a Riemann surface are well known to have a symplectic (in fact K\"{a}hler) structure. We show this symplectic structure explictly and proceed to show a family of symplectic (in fact, K\"{a}hler) structures $\Omega_{\Psi_0}$ on the moduli space, parametrised by $\Psi_0$, a section of a line bundle on the Riemann surface. Next we show that corresponding to these there is a family of prequantum line bundles ${\mathcal P}_{\Psi_0}$on the moduli space whose curvature is proportional to the symplectic forms $\Omega_{\Psi_0}$.Comment: 8 page

Spectroscopic Confirmation of a Protocluster at z=3.786

We present new observations of the field containing the z=3.786 protocluster, PC217.96+32.3. We confirm that it is one of the largest and most overdense high-redshift structures known. Such structures are rare even in the largest cosmological simulations. We used the Mayall/MOSAIC1.1 imaging camera to image a 1.2x0.6 deg area (~150x75 comoving Mpc) surrounding the protocluster's core and discovered 165 candidate Lyman Alpha emitting galaxies (LAEs) and 788 candidate Lyman Break galaxies (LBGs). There are at least 2 overdense regions traced by the LAEs, the largest of which shows an areal overdensity in its core (i.e., within a radius of 2.5 comoving Mpc) of 14+/-7 relative to the average LAE spatial density in the imaged field. Further, the average LAE spatial density in the imaged field is twice that derived by other field LAE surveys. Spectroscopy with Keck/DEIMOS yielded redshifts for 164 galaxies (79 LAEs and 85 LBGs); 65 lie at a redshift of 3.785+/-0.010. The velocity dispersion of galaxies near the core is 350+/-40 km/s, a value robust to selection effects. The overdensities are likely to collapse into systems with present-day masses of >10^{15} solar masses and >6x10^{14} solar masses. The low velocity dispersion may suggest a dynamically young protocluster. We find a weak trend between narrow-band (Lyman Alpha) luminosity and environmental density: the Lyman Alpha luminosity is enhanced on average by 1.35X within the protocluster core. There is no evidence that the Lyman Alpha equivalent width depends on environment. These suggest that star-formation and/or AGN activity is enhanced in the higher density regions of the structure. PC217.96+32.3 is a Coma cluster analog, witnessed in the process of formation.Comment: Accepted for publication in the Astrophysical Journal (March 27, 2016

Spin Hall effect in a Kagome lattice driven by Rashba spin-orbit interaction

Using four-terminal Landauer-B\"{u}ttiker formalism and Green's function technique, in this present paper, we calculate numerically spin Hall conductance (SHC) and longitudinal conductance of a finite size kagome lattice with Rashba spin-orbit (SO) interaction both in presence and absence of external magnetic flux in clean limit. In the absence of magnetic flux, we observe that depending on the Fermi surface topology of the system SHC changes its sign at different values of Fermi energy, along with the band center. Unlike the infinite system (where SHC is a universal constant $\pm \frac{e}{8 \pi}$), here SHC depends on the external parameters like SO coupling strength, Fermi energy, etc. We show that in the presence of any arbitrary magnetic flux, periodicity of the system is lost and the features of SHC tends to get reduced because of elastic scattering. But again at some typical values of flux ($\phi=1/2, 1/4, 3/4..., etc.) the system retains its periodicity depending on its size and the features of spin Hall effect (SHE) reappears. Our predicted results may be useful in providing a deeper insight into the experimental realization of SHE in such geometries.Comment: 10 pages, 10 figure

Magneto-transport in a mesoscopic ring with Rashba and Dresselhaus spin-orbit interactions

Electronic transport in a one-dimensional mesoscopic ring threaded by a magnetic flux is studied in presence of Rashba and Dresselhaus spin-orbit interactions. A completely analytical technique within a tight-binding formalism unveils the spin-split bands in presence of the spin-orbit interactions and leads to a method of determining the strength of the Dresselhaus interaction. In addition to this, the persistent currents for ordered and disordered rings have been investigated numerically. It is observed that, the presence of the spin-orbit interaction, in general, leads to an enhanced amplitude of the persistent current. Numerical results corroborate the respective analytical findings.Comment: 7 pages, 7 figure