New Global Minima for Thomson's Problem of Charges on a Sphere

Using numerical arguments we find that for $N$ = 306 a tetrahedral configuration ($T_h$) and for N=542 a dihedral configuration ($D_5$) are likely the global energy minimum for Thomson's problem of minimizing the energy of $N$ unit charges on the surface of a unit conducting sphere. These would be the largest $N$ by far, outside of the icosadeltahedral series, for which a global minimum for Thomson's problem is known. We also note that the current theoretical understanding of Thomson's problem does not rule out a symmetric configuration as the global minima for N=306 and 542. We explicitly find that analogues of the tetrahedral and dihedral configurations for $N$ larger than 306 and 542, respectively, are not global minima, thus helping to confirm the theory of Dodgson and Moore (Phys. Rev. B 55, 3816 (1997)) that as $N$ grows dislocation defects can lower the lattice strain of symmetric configurations and concomitantly the energy. As well, making explicit previous work by ourselves and others, for $N<1000$ we give a full accounting of icosadeltahedral configuration which are not global minima and those which appear to be, and discuss how this listing and our results for the tetahedral and dihedral configurations may be used to refine theoretical understanding of Thomson's problem.Comment: 1- Manuscript revised. 2- A new global minimum found for a dihedral (D_5) configuration found for N=54

A Novel Symmetric Four Dimensional Polytope Found Using Optimization Strategies Inspired by Thomson's Problem of Charges on a Sphere

Inspired by, and using methods of optimization derived from classical three dimensional electrostatics, we note a novel beautiful symmetric four dimensional polytope we have found with 80 vertices. We also describe how the method used to find this symmetric polytope, and related methods can potentially be used to find good examples for the kissing and packing problems in D dimensions

Influence of Dislocations in Thomson's Problem

We investigate Thomson's problem of charges on a sphere as an example of a system with complex interactions. Assuming certain symmetries we can work with a larger number of charges than before. We found that, when the number of charges is large enough, the lowest energy states are not those with the highest symmetry. As predicted previously by Dodgson and Moore, the complex patterns in these states involve dislocation defects which screen the strains of the twelve disclinations required to satisfy Euler's theorem.Comment: 9 pages, 4 figures in gif format. Original PS files can be obtained in http://fermi.fcu.um.es/thomso

Numerical study of relaxation in electron glasses

We perform a numerical simulation of energy relaxation in three-dimensional electron glasses in the strongly localized regime at finite temperatures. We consider systems with no interactions, with long-range Coulomb interactions and with short-range interactions, obtaining a power law relaxation with an exponent of 0.15, which is independent of the parameters of the problem and of the type of interaction. At very long times, we always find an exponential regime whose characteristic time strongly depends on temperature, system size, interaction type and localization radius. We extrapolate the longest relaxation time to macroscopic sizes and, for interacting samples, obtain values much larger than the measuring time. We finally study the number of electrons participating in the relaxation processes of very low energy configurations.Comment: 6 eps figures. To be published in Phys. Rev.

Symmetries in Fluctuations Far from Equilibrium

Fluctuations arise universally in Nature as a reflection of the discrete microscopic world at the macroscopic level. Despite their apparent noisy origin, fluctuations encode fundamental aspects of the physics of the system at hand, crucial to understand irreversibility and nonequilibrium behavior. In order to sustain a given fluctuation, a system traverses a precise optimal path in phase space. Here we show that by demanding invariance of optimal paths under symmetry transformations, new and general fluctuation relations valid arbitrarily far from equilibrium are unveiled. This opens an unexplored route toward a deeper understanding of nonequilibrium physics by bringing symmetry principles to the realm of fluctuations. We illustrate this concept studying symmetries of the current distribution out of equilibrium. In particular we derive an isometric fluctuation relation which links in a strikingly simple manner the probabilities of any pair of isometric current fluctuations. This relation, which results from the time-reversibility of the dynamics, includes as a particular instance the Gallavotti-Cohen fluctuation theorem in this context but adds a completely new perspective on the high level of symmetry imposed by time-reversibility on the statistics of nonequilibrium fluctuations. The new symmetry implies remarkable hierarchies of equations for the current cumulants and the nonlinear response coefficients, going far beyond Onsager's reciprocity relations and Green-Kubo formulae. We confirm the validity of the new symmetry relation in extensive numerical simulations, and suggest that the idea of symmetry in fluctuations as invariance of optimal paths has far-reaching consequences in diverse fields.Comment: 8 pages, 4 figure

Discovery of a wide companion near the deuterium burning mass limit in the Upper Scorpius association

We present the discovery of a companion near the deuterium burning mass limit located at a very wide distance, at an angular separation of 4.6+/-0.1 arcsec (projected distance of ~ 670 AU) from UScoCTIO108, a brown dwarf of the very young Upper Scorpius association. Optical and near-infrared photometry and spectroscopy confirm the cool nature of both objects, with spectral types of M7 and M9.5, respectively, and that they are bona fide members of the association, showing low gravity and features of youth. Their masses, estimated from the comparison of their bolometric luminosities and theoretical models for the age range of the association, are 60+/-20 and 14^{+2}_{-8} MJup, respectively. The existence of this object around a brown dwarf at this wide orbit suggests that the companion is unlikely to have formed in a disk based on current planet formation models. Because this system is rather weakly bound, they did not probably form through dynamical ejection of stellar embryos.Comment: 10 pages, including 4 figures and 2 table

Interstitial Fractionalization and Spherical Crystallography

Finding the ground states of identical particles packed on spheres has relevance for stabilizing emulsions and a venerable history in the literature of theoretical physics and mathematics. Theory and experiment have confirmed that defects such as disclinations and dislocations are an intrinsic part of the ground state. Here we discuss the remarkable behavior of vacancies and interstitials in spherical crystals. The strain fields of isolated disclinations forced in by the spherical topology literally rip interstitials and vacancies apart, typically into dislocation fragments that combine with the disclinations to create small grain boundary scars. The fractionation is often into three charge-neutral dislocations, although dislocation pairs can be created as well. We use a powerful, freely available computer program to explore interstitial fractionalization in some detail, for a variety of power law pair potentials. We investigate the dependence on initial conditions and the final state energies, and compare the position dependence of interstitial energies with the predictions of continuum elastic theory on the sphere. The theory predicts that, before fragmentation, interstitials are repelled from 5-fold disclinations and vacancies are attracted. We also use vacancies and interstitials to study low energy states in the vicinity of "magic numbers" that accommodate regular icosadeltahedral tessellations.Comment: 21 pages, 9 figure

VLT X-shooter spectroscopy of the nearest brown dwarf binary

The aim of the project is to characterise both components of the nearest brown dwarf sytem to the Sun, WISE J104915.57-531906.1 (=Luhman16AB) at optical and near-infrared wavelengths. We obtained high signal-to-noise intermediate-resolution (R~6000-11000) optical (600-1000 nm) and near-infrared (1000-2480nm) spectra of each component of Luhman16AB, the closest brown dwarf binary to the Sun, with the X-Shooter instrument on the Very Large Telescope. We classify the primary and secondary of the Luhman16 system as L6-L7.5 and T0+/-1, respectively, in agreement with previous measurements published in the literature. We present measurements of the lithium pseudo-equivalent widths, which appears of similar strength on both components (8.2+/-1.0 Angstroms and 8.4+/-1.5 Angstroms for the L and T components, respectively). The presence of lithium (Lithium 7) in both components imply masses below 0.06 Msun while comparison with models suggests lower limits of 0.04 Msun. The detection of lithium in the T component is the first of its kind. Similarly, we assess the strength of other alkali lines (e.g. pseudo-equivalent widths of 6-7 Angstroms for RbI and 4-7 Angstroms for CsI) present in the optical and near-infrared regions and compare with estimates for L and T dwarfs. We also derive effective temperatures and luminosities of each component of the binary: -4.66+/-0.08 dex and 1305(+180)(-135) for the L dwarf and -4.68+/-0.13 dex and 1320(+185)(-135) for the T dwarf, respectively. Using our radial velocity determinations, the binary does not appear to belong to any of the well-known moving group. Our preliminary theoretical analysis of the optical and J-band spectra indicates that the L- and T-type spectra can be reproduced with a single temperature and gravity but different relative chemical abundances which impact strongly the spectral energy distribution of L/T transition objects.Comment: 12 pages, 9 figure, 3 tables, accepted to A&