Defect free global minima in Thomson's problem of charges on a sphere

Given $N$ unit points charges on the surface of a unit conducting sphere, what configuration of charges minimizes the Coulombic energy $\sum_{i>j=1}^N 1/r_{ij}$? Due to an exponential rise in good local minima, finding global minima for this problem, or even approaches to do so has proven extremely difficult. For \hbox{$N = 10(h^2+hk+k^2)+ 2$} recent theoretical work based on elasticity theory, and subsequent numerical work has shown, that for $N \sim >500$--1000 adding dislocation defects to a symmetric icosadeltahedral lattice lowers the energy. Here we show that in fact this approach holds for all $N$, and we give a complete or near complete catalogue of defect free global minima.Comment: Revisions in Tables and Reference

The Exchange Gate in Solid State Spin Quantum Computation: The Applicability of the Heisenberg Model

Solid state quantum computing proposals rely on adiabatic operations of the exchange gate among localized spins in nanostructures. We study corrections to the Heisenberg interaction between lateral semiconductor quantum dots in an external magnetic field. Using exact diagonalization we obtain the regime of validity of the adiabatic approximation. We also find qualitative corrections to the Heisenberg model at high magnetic fields and in looped arrays of spins. Looped geometries of localized spins generate flux dependent, multi-spin terms which go beyond the basic Heisenberg model.Comment: 13 pages, 8 figure

About the determination of critical exponents related to possible phase transitions in nuclear fragmentation

We introduce a method based on the finite size scaling assumption which allows to determine numerically the critical point and critical exponents related to observables in an infinite system starting from the knowledge of the observables in finite systems. We apply the method to bond percolation in 2 dimensions and compare the results obtained when the bond probability p or the fragment multiplicity m are chosen as the relevant parameter.Comment: 12 pages, TeX, 4 figure

Implications of sterile neutrinos for medium/long-baseline neutrino experiments and the determination of θ13\theta_{13}

We revisit some of the recent neutrino observations and anomalies in the context of sterile neutrinos. Based on a general parametrization motivated in the presence of sterile neutrinos, the consistency of the MINOS disappearance data with additional sterile neutrinos is discussed. We also explore the implications of sterile neutrinos for the measurement of $|U_{\mu3}|$ in this case. Regarding the determination of $|U_{e3}|$, we observe that the existence of sterile neutrinos may induce a significant modification of the $\theta_{13}$ angle in neutrino appearance experiments like T2K and MINOS, over and above the ambiguities and degeneracies that are already present in 3-neutrino parameter extractions. The modification is less significant in reactor neutrino experiments like Double-CHOOZ, Daya Bay and RENO and therefore the extracted $|U_{e3}|$ value when sterile neutrinos are present is close to the one that would be obtained in the 3-neutrino case. We also conclude that the results from T2K imply a 90% C.L. lower-bound on $|U_{e3}|$, in the "$\,3+2$" neutrino case, which is still within the sensitivity of future reactor neutrino experiments like Daya Bay, and consistent with the one-$\sigma$ range of $\sin^22\theta_{13}$ recently reported by the Double-CHOOZ experiment. Finally, we argue that for the recently determined best-fit parameters, the results in the "$\,3+1$" scenario would be very close to the medium/long baseline results obtained in the "$\,3+2$" case analyzed in this work.Comment: 25 pages, 9 figures, revtex4-1. Typos corrected, published versio