Bose Einstein Condensation of incommensurate solid 4He

It is pointed out that simulation computation of energy performed so far cannot be used to decide if the ground state of solid 4He has the number of lattice sites equal to the number of atoms (commensurate state) or if it is different (incommensurate state). The best variational wave function, a shadow wave function, gives an incommensurate state but the equilibrium concentration of vacancies remains to be determined. In order to investigate the presence of a supersolid phase we have computed the one--body density matrix in solid 4He for the incommensurate state by means of the exact Shadow Path Integral Ground State projector method. We find a vacancy induced Bose Einstein condensation of about 0.23 atoms per vacancy at a pressure of 54 bar. This means that bulk solid 4He is supersolid at low enough temperature if the exact ground state is incommensurate.Comment: 5 pages, 2 figure

The electronic structure of liquid water within density functional theory

In the last decade, computational studies of liquid water have mostly concentrated on ground state properties. However recent spectroscopic measurements have been used to infer the structure of water, and the interpretation of optical and x-ray spectra requires accurate theoretical models of excited electronic states, not only of the ground state. To this end, we investigate the electronic properties of water at ambient conditions using ab initio density functional theory within the generalized gradient approximation (DFT/GGA), focussing on the unoccupied subspace of Kohn-Sham eigenstates. We generate long (250 ps) classical trajectories for large supercells, up to 256 molecules, from which uncorrelated configurations of water molecules are extracted for use in DFT/GGA calculations of the electronic structure. We find that the density of occupied states of this molecular liquid is well described with 32 molecule supercells using a single k-point (k = 0) to approximate integration over the first Brillouin zone. However, the description of the density of unoccupied states (u-EDOS) is sensitive to finite size effects. Small, 32 molecule supercell calculations, using Gamma-the point approximation, yield a spuriously isolated state above the Fermi level. Nevertheless, the more accurate u-EDOS of large, 256 molecule supercells may be reproduced using smaller supercells and increased k-point sampling. This indicates that the electronic structure of molecular liquids like water is relatively insensitive to the long-range disorder in the molecular structure. These results have important implications for efficiently increasing the accuracy of spectral calculations for water and other molecular liquids.Comment: 12 pages, 11 figures (low quality) Submitted to JChemPhy

Band structure and optical properties of opal photonic crystals

A theoretical approach for the interpretation of reflectance spectra of opal photonic crystals with fcc structure and (111) surface orientation is presented. It is based on the calculation of photonic bands and density of states corresponding to a specified angle of incidence in air. The results yield a clear distinction between diffraction in the direction of light propagation by (111) family planes (leading to the formation of a stop band) and diffraction in other directions by higher-order planes (corresponding to the excitation of photonic modes in the crystal). Reflectance measurements on artificial opals made of self-assembled polystyrene spheres are analyzed according to the theoretical scheme and give evidence of diffraction by higher-order crystalline planes in the photonic structure.Comment: to appear in PR

Sub-structure formation in starless cores

Motivated by recent observational searches of sub-structure in starless molecular cloud cores, we investigate the evolution of density perturbations on scales smaller than the Jeans length embedded in contracting isothermal clouds, adopting the same formalism developed for the expanding Universe and the solar wind. We find that initially small amplitude, Jeans-stable perturbations (propagating as sound waves in the absence of a magnetic field), are amplified adiabatically during the contraction, approximately conserving the wave action density, until they either become nonlinear and steepen into shocks at a time $t_{\rm nl}$, or become gravitationally unstable when the Jeans length decreases below the scale of the perturbations at a time $t_{\rm gr}$. We evaluate analytically the time $t_{\rm nl}$ at which the perturbations enter the non-linear stage using a Burgers' equation approach, and we verify numerically that this time marks the beginning of the phase of rapid dissipation of the kinetic energy of the perturbations. We then show that for typical values of the rms Mach number in molecular cloud cores, $t_{\rm nl}$ is smaller than $t_{\rm gr}$, and therefore density perturbations likely dissipate before becoming gravitational unstable. Solenoidal modes grow at a faster rate than compressible modes, and may eventually promote fragmentation through the formation of vortical structures.Comment: 8 pages, 4 figure

Dynamic Leadership: Toolbox for the Values-Based Entrepreneur

Four entrepreneurship models are proposed which lend guidance in the development of a business, from birth to exit, each examining ways to maintain the business founder’s initial vision and to continue to infuse values and ethical decision-making at each stage of development