Diagonal quantum Bianchi type IX models in N=1 supergravity

We take the general quantum constraints of N=1 supergravity in the special case of a Bianchi metric, with gravitino fields constant in the invariant basis. We construct the most general possible wave function which solves the Lorentz constraints and study the supersymmetry constraints in the Bianchi Class A Models. For the Bianchi-IX cases, both the Hartle-Hawking state and wormhole state are found to exist in the middle fermion levels.Comment: plain LaTex, 17 pages, accepted for publication in Classical Quantum Gravit

Production, Competition Indices, and Nutritive Values of Setaria Splendida, Centrosema Pubescens, and Clitoria Ternatea in Mixed Cropping Systems in Peatland

This research was conducted to evaluate production, different competition indices and nutritive value of Setaria splendida, Centrosema pubescens, and Clitoria ternatea in monoculture and mix cropping system on peat soil land. The experiment was set up in a randomized complete block design with five treatments and three replications. The five treatments were: S. splendida sole cropping (SS), C. pubescens sole cropping (CP), C. ternatea sole cropping (CT), S. splendida and C. pubescens mix cropping (SS/CP) and S. splendida/C. ternatea mix cropping (SS/CT). The DM yield of S. splendida in mixed cropping with C. pubescens increased 43.4% and in mix cropping with C. ternatea increased 15.7% compared to sole S. splendida. The value of land equivalent ratio of SS/CP (LERSS/CP) was >1. The LERSS/CT value was <1. The crowding coefficient value of S. splendida (KSS) was higher than KCP and KCT. The total value of KSS/CP and KSS/CT were >1. The competition ratio (CR) values of S. splendida in both mix cropping were >1. The agressivity (A) values of S. splendida in both mix cropping were positive. The crude protein, NDF and ADF content of forage were not affected by mix cropping system. In conclusion, mix cropping in peatland do not affect productivity and nutritive value of S. splendida, C. pubescens, and C. ternatea. S. splendida is more effective in exploiting environmental resources when intercropped with C. pubescens compared to C. ternatea on peatland

How to identify the youngest protostars

We study the transition from a prestellar core to a Class 0 protostar, using SPH to simulate the dynamical evolution, and a Monte Carlo radiative transfer code to generate the SED and isophotal maps. For a prestellar core illuminated by the standard interstellar radiation field, the luminosity is low and the SED peaks at ~190 micron. Once a protostar has formed, the luminosity rises (due to a growing contribution from accretion onto the protostar) and the peak of the SED shifts to shorter wavelengths (~80-100 micron). However, by the end of the Class 0 phase, the accretion rate is falling, the luminosity has decreased, and the peak of the SED shifts back towards longer wavelengths (90-150 micron). In our simulations, the density of material around the protostar remains sufficiently high well into the Class 0 phase that the protostar only becomes visible in the NIR if it is displaced from the centre dynamically. Raw submm/mm maps of Class 0 protostars tend to be much more centrally condensed than those of prestellar cores. However, when convolved with a typical telescope beam, the difference in central concentration is less marked, although the Class 0 protostars appear more circular. Our results suggest that, if a core is deemed to be prestellar on the basis of having no associated IRAS source, no cm radio emission, and no outflow, but it has a circular appearance and an SED which peaks at wavelengths below ~170 micron, it may well contain a very young Class 0 protostar.Comment: Accepted by A&A (avaliable with high-res images at http://carina.astro.cf.ac.uk/pub/Dimitrios.Stamatellos/publications

Dynamics of a nanomechanical resonator coupled to a superconducting single-electron transistor

We present an analysis of the dynamics of a nanomechanical resonator coupled to a superconducting single electron transistor (SSET) in the vicinity of the Josephson quasiparticle (JQP) and double Josephson quasiparticle (DJQP) resonances. For weak coupling and wide separation of dynamical timescales, we find that for either superconducting resonance the dynamics of the resonator is given by a Fokker-Planck equation, i.e., the SSET behaves effectively as an equilibrium heat bath, characterised by an effective temperature, which also damps the resonator and renormalizes its frequency. Depending on the gate and drain-source voltage bias points with respect to the superconducting resonance, the SSET can also give rise to an instability in the mechanical resonator marked by negative damping and temperature within the appropriate Fokker-Planck equation. Furthermore, sufficiently close to a resonance, we find that the Fokker-Planck description breaks down. We also point out that there is a close analogy between coupling a nanomechanical resonator to a SSET in the vicinity of the JQP resonance and Doppler cooling of atoms by means of lasers

Restoring Time Dependence into Quantum Cosmology

Mini superspace cosmology treats the scale factor $a(t)$, the lapse function $n(t)$, and an optional dilation field $\phi(t)$ as canonical variables. While pre-fixing $n(t)$ means losing the Hamiltonian constraint, pre-fixing $a(t)$ is serendipitously harmless at this level. This suggests an alternative to the Hartle-Hawking approach, where the pre-fixed $a(t)$ and its derivatives are treated as explicit functions of time, leaving $n(t)$ and a now mandatory $\phi(t)$ to serve as canonical variables. The naive gauge pre-fix $a(t)=const$ is clearly forbidden, causing evolution to freeze altogether, so pre-fixing the scale factor, say $a(t)=t$, necessarily introduces explicit time dependence into the Lagrangian. Invoking Dirac's prescription for dealing with constraints, we construct the corresponding mini superspace time dependent total Hamiltonian, and calculate the Dirac brackets, characterized by $\{n,\phi\}_D\neq 0$, which are promoted to commutation relations in the quantum theory.Comment: Honorable Mentioned essay - Gravity Research Foundation 201

Electronic properties of gated triangular graphene quantum dots: Magnetism, correlations, and geometrical effects

We present a theory of electronic properties of gated triangular graphene quantum dots with zigzag edges as a function of size and carrier density. We focus on electronic correlations, spin and geometrical effects using a combination of atomistic tight-binding, Hartree-Fock and configuration interaction methods (TB+HF+CI) including long range Coulomb interactions. The single particle energy spectrum of triangular dots with zigzag edges exhibits a degenerate shell at the Fermi level with a degeneracy N_{edge} proportional to the edge size. We determine the effect of the electron-electron interactions on the ground state, the total spin and the excitation spectrum as a function of a shell filling and the degeneracy of the shell using TB+HF+CI for N_{edge} < 12 and approximate CI method for N_{edge}\geq 12. For a half-filled neutral shell we find spin polarized ground state for structures up to N=500 atoms in agreement with previous {\it ab initio} and mean-field calculations, and in agreement with Lieb's theorem for a Hubbard model on a bipartite lattice. Adding a single electron leads to the complete spin depolarization for N_{edge}\leq 9. For larger structures, the spin depolarization is shown to occur at different filling factors. Away from half-fillings excess electrons(holes) are shown to form Wigner-like spin polarized triangular molecules corresponding to large gaps in the excitation spectrum. The validity of conclusions is assessed by a comparison of results obtained from different levels of approximations. While for the charge neutral system all methods give qualitatively similar results, away from the charge neutrality an inclusion of all Coulomb scattering terms is necessary to produce results presented here.Comment: 13 pages, 13 figure

Note on Logarithmic Switchback Terms in Regular and Singular Perturbation Expansions

The occurrence of logarithmic switchback is studied for ordinary differential equations containing a parameter k which is allowed to take any value in a continuum of real numbers and with boundary conditions imposed at x = ε and x = ∞. Classical theory tells us that if the equation has a regular singular point at the origin there is a family of solutions which varies continuously with k, and the expansion around the origin has log x terms for a discrete set of values of k. It is shown here how nonlinearity enlarges this set so that it may even be dense in some interval of the real numbers. A log x term in the expansion in x leads to expansion coefficients containing log ε (switchback) in the perturbation expansion. If for a given value of k logarithmic terms in x and ε occur they may be obtained by continuity from neighboring values of k. Switchback terms occurred conspicuously in singular-perturbation solutions of problems posed for semi-infinite domain x ≥ ε. This connection is historical rather than logical. In particular we study here switchback terms for a specific example using methods of both singular and regular perturbations