Spin-guides and spin-splitters: Waveguide analogies in one-dimensional spin chains

Here we show a direct mapping between waveguide theory and spin chain transport, opening an alternative approach to quantum information transport in the solid-state. By applying temporally varying control profiles to a spin chain, we design a virtual waveguide or 'spin-guide' to conduct individual spin excitations along defined space-time trajectories of the chain. We explicitly show that the concepts of confinement, adiabatic bend loss and beamsplitting can be mapped from optical waveguide theory to spin-guides (and hence 'spin-splitters'). Importantly, the spatial scale of applied control pulses is required to be large compared to the inter-spin spacing, and thereby allowing the design of scalable control architectures.Comment: 5 figure

Dark Matter Scaling Relations

We establish the presence of a dark matter core radius, for the first time in a very large number of spiral galaxies of all luminosities. Contrary to common opinion we find that the sizes of these cores and the " DM core problem" are bigger for more massive spirals. As a result the Burkert profile provides an excellent mass model for dark halos around disk galaxies. Moreover, we find that the spiral dark matter core densities $\rho_{0}$ and core radii $r_{0}$ lie in the same scaling relation $\rho_{0}=4.5\times 10^-2 (r_{0}/kpc)^{-2/3} M_{\odot}pc^{-3}$ of dwarf galaxies with core radii upto ten times more smaller.Comment: 4 pages, 4 figures, Accepted for Publication in Apj Let

A network-based ranking system for American college football

American college football faces a conflict created by the desire to stage national championship games between the best teams of a season when there is no conventional playoff system to decide which those teams are. Instead, ranking of teams is based on their record of wins and losses during the season, but each team plays only a small fraction of eligible opponents, making the system underdetermined or contradictory or both. It is an interesting challenge to create a ranking system that at once is mathematically well-founded, gives results in general accord with received wisdom concerning the relative strengths of the teams, and is based upon intuitive principles, allowing it to be accepted readily by fans and experts alike. Here we introduce a one-parameter ranking method that satisfies all of these requirements and is based on a network representation of college football schedules.Comment: 15 pages, 3 figure

Modal Approach to Casimir Forces in Periodic Structures

We present a modal approach to calculate finite temperature Casimir interactions between two periodically modulated surfaces. The scattering formula is used and the reflection matrices of the patterned surfaces are calculated decomposing the electromagnetic field into the natural modes of the structures. The Casimir force gradient from a deeply etched silicon grating is evaluated using the modal approach and compared to experiment for validation. The Casimir force from a two dimensional periodic structure is computed and deviations from the proximity force approximation examined.Comment: 13 pages, 7 figure

Cosmological Feedback from High-Redshift Dwarf Galaxies

We model how repeated supernova explosions in high-redshift dwarf starburst galaxies drive superbubbles and winds out of the galaxies. We compute the efficiencies of metal and mass ejection and energy transport from the galactic potentials, including the effect of cosmological infall of external gas. The starburst bubbles quickly blow out of small, high-redshift, galactic disks, but must compete with the ram pressure of the infalling gas to escape into intergalactic space. We show that the assumed efficiency of the star formation rate dominates the bubble evolution and the metal, mass, and energy feedback efficiencies. With star formation efficiency f*=0.01, the ram pressure of infall can confine the bubbles around high-redshift dwarf galaxies with circular velocities v_c>52 km/s. We can expect high metal and mass ejection efficiencies, and moderate energy transport efficiencies in halos with v_c~30-50 km/s and f*~0.01 as well as in halos with v_c~100 km/s and f*>>0.01. Such haloes collapse successively from 1-2 sigma peaks in LambdaCDM Gaussian density perturbations as time progresses. These dwarf galaxies can probably enrich low and high-density regions of intergalactic space with metals to 10^-3-10^-2 Zsun as they collapse at z~8 and z<5 respectively. They also may be able to provide adequate turbulent energy to prevent the collapse of other nearby halos, as well as to significantly broaden Lyman-alpha absorption lines to v_rms~20-40 km/s. We compute the timescales for the next starbursts if gas freely falls back after a starburst, and find that, for star formation efficiencies as low as f*<0.01, the next starburst should occur in less than half the Hubble time at the collapse redshift. This suggests that episodic star formation may be ubiquitous in dwarf galaxies.Comment: Accepted for ApJ v613, 60 pages, 15 figure

The negatively charged nitrogen-vacancy centre in diamond: the electronic solution

The negatively charged nitrogen-vacancy centre is a unique defect in diamond that possesses properties highly suited to many applications, including quantum information processing, quantum metrology, and biolabelling. Although the unique properties of the centre have been extensively documented and utilised, a detailed understanding of the physics of the centre has not yet been achieved. Indeed there persists a number of points of contention regarding the electronic structure of the centre, such as the ordering of the dark intermediate singlet states. Without a sound model of the centre's electronic structure, the understanding of the system's unique dynamical properties can not effectively progress. In this work, the molecular model of the defect centre is fully developed to provide a self consistent model of the complete electronic structure of the centre. The application of the model to describe the effects of electric, magnetic and strain interactions, as well as the variation of the centre's fine structure with temperature, provides an invaluable tool to those studying the centre and a means to design future empirical and ab initio studies of this important defect.Comment: 24 pages, 6 figures, 10 table