Velocity of sound in a Bose-Einstein condensate in the presence of an optical lattice and transverse confinement

We study the effect of the transverse degrees of freedom on the velocity of sound in a Bose-Einstein condensate immersed in a one-dimensional optical lattice and radially confined by a harmonic trap. We compare the results of full three-dimensional calculations with those of an effective 1D model based on the equation of state of the condensate. The perfect agreement between the two approaches is demonstrated for several optical lattice depths and throughout the full crossover from the 1D mean-field to the Thomas Fermi regime in the radial direction.Comment: final versio

Transition to an Insulating Phase Induced by Attractive Interactions in the Disordered Three-Dimensional Hubbard Model

We study numerically the interplay of disorder and attractive interactions for spin-1/2 fermions in the three-dimensional Hubbard model. The results obtained by projector quantum Monte Carlo simulations show that at moderate disorder, increasing the attractive interaction leads to a transition from delocalized superconducting states to the insulating phase of localized pairs. This transition takes place well within the metallic phase of the single-particle Anderson model.Comment: revtex, 4 pages, 3 figure

Approximate k-state solutions to the Dirac-Yukawa problem based on the spin and pseudospin symmetry

Using an approximation scheme to deal with the centrifugal (pseudo-centrifugal) term, we solve the Dirac equation with the screened Coulomb (Yukawa) potential for any arbitrary spin-orbit quantum number {\kappa}. Based on the spin and pseudospin symmetry, analytic bound state energy spectrum formulas and their corresponding upper- and lower-spinor components of two Dirac particles are obtained using a shortcut of the Nikiforov-Uvarov method. We find a wide range of permissible values for the spin symmetry constant C_{s} from the valence energy spectrum of particle and also for pseudospin symmetry constant C_{ps} from the hole energy spectrum of antiparticle. Further, we show that the present potential interaction becomes less (more) attractive for a long (short) range screening parameter {\alpha}. To remove the degeneracies in energy levels we consider the spin and pseudospin solution of Dirac equation for Yukawa potential plus a centrifugal-like term. A few special cases such as the exact spin (pseudospin) symmetry Dirac-Yukawa, the Yukawa plus centrifugal-like potentials, the limit when {\alpha} becomes zero (Coulomb potential field) and the non-relativistic limit of our solution are studied. The nonrelativistic solutions are compared with those obtained by other methods.Comment: 21 pages, 6 figure

Nonlinear time-series analysis of Hyperion's lightcurves

Hyperion is a satellite of Saturn that was predicted to remain in a chaotic rotational state. This was confirmed to some extent by Voyager 2 and Cassini series of images and some ground-based photometric observations. The aim of this aticle is to explore conditions for potential observations to meet in order to estimate a maximal Lyapunov Exponent (mLE), which being positive is an indicator of chaos and allows to characterise it quantitatively. Lightcurves existing in literature as well as numerical simulations are examined using standard tools of theory of chaos. It is found that existing datasets are too short and undersampled to detect a positive mLE, although its presence is not rejected. Analysis of simulated lightcurves leads to an assertion that observations from one site should be performed over a year-long period to detect a positive mLE, if present, in a reliable way. Another approach would be to use 2---3 telescopes spread over the world to have observations distributed more uniformly. This may be achieved without disrupting other observational projects being conducted. The necessity of time-series to be stationary is highly stressed.Comment: 34 pages, 12 figures, 4 tables; v2 after referee report; matches the version accepted in Astrophysics and Space Scienc

A terminal assessment of stages theory : introducing a dynamic states approach to entrepreneurship

Stages of Growth models were the most frequent theoretical approach to understanding entrepreneurial business growth from 1962 to 2006; they built on the growth imperative and developmental models of that time. An analysis of the universe of such models (N=104) published in the management literature shows no consensus on basic constructs of the approach, nor is there any empirical confirmations of stages theory. However, by changing two propositions of the stages models, a new dynamic states approach is derived. The dynamic states approach has far greater explanatory power than its precursor, and is compatible with leading edge research in entrepreneurship

New exact solution of Dirac-Coulomb equation with exact boundary condition

It usually writes the boundary condition of the wave equation in the Coulomb field as a rough form without considering the size of the atomic nucleus. The rough expression brings on that the solutions of the Klein-Gordon equation and the Dirac equation with the Coulomb potential are divergent at the origin of the coordinates, also the virtual energies, when the nuclear charges number Z > 137, meaning the original solutions do not satisfy the conditions for determining solution. Any divergences of the wave functions also imply that the probability density of the meson or the electron would rapidly increase when they are closing to the atomic nucleus. What it predicts is not a truth that the atom in ground state would rapidly collapse to the neutron-like. We consider that the atomic nucleus has definite radius and write the exact boundary condition for the hydrogen and hydrogen-like atom, then newly solve the radial Dirac-Coulomb equation and obtain a new exact solution without any mathematical and physical difficulties. Unexpectedly, the K value constructed by Dirac is naturally written in the barrier width or the equivalent radius of the atomic nucleus in solving the Dirac equation with the exact boundary condition, and it is independent of the quantum energy. Without any divergent wave function and the virtual energies, we obtain a new formula of the energy levels that is different from the Dirac formula of the energy levels in the Coulomb field.Comment: 12 pages,no figure

Generalized Spin and Pseudo-Spin Symmetry: Relativistic Extension of Supersymmetric Quantum Mechanics

We consider the Dirac equation in 1+1 space-time dimension with vector, scalar and pseudo-scalar coupling. In the traditional spin (or pseudo-spin) symmetry, the difference between (or sum of) the scalar and vector potentials is a constant. Here, however, we introduce an alternative symmetry where the scalar or pseudo-scalar potential is proportional to the vector potential. This leads to a model with significant extensions to supersymmetric quantum mechanics. We present a formal solution of the problem but give explicit analytic results for specific examples.Comment: 9 page

Heavy Quark Photoproduction in Ultra-peripheral Heavy Ion Collisions

Heavy quarks are copiously produced in ultra-peripheral heavy ion collisions. In the strong electromagnetic fields, c c-bar and b b-bar are produced by photonuclear and two-photon interactions; hadroproduction can occur in grazing interactions. We present the total cross sections, quark transverse momentum and rapidity distributions, as well as the Q Q-bar invariant mass spectra from the three production channels. We consider AA and pA collisions at the Relativistic Heavy Ion Collider and Large Hadron Collider. We discuss techniques for separating the three processes and describe how the AA to pA production ratios might be measured accurately enough to study nuclear shadowing.Comment: Minor changes to satisfy referees and typo fixes; 52 pages including 17 figure

Evolution of electronic and ionic structure of Mg-clusters with the growth cluster size

The optimized structure and electronic properties of neutral and singly charged magnesium clusters have been investigated using ab initio theoretical methods based on density-functional theory and systematic post-Hartree-Fock many-body perturbation theory accounting for all electrons in the system. We have systematically calculated the optimized geometries of neutral and singly charged magnesium clusters consisting of up to 21 atoms, electronic shell closures, binding energies per atom, ionization potentials and the gap between the highest occupied and the lowest unoccupied molecular orbitals. We have investigated the transition to the hcp structure and metallic evolution of the magnesium clusters, as well as the stability of linear chains and rings of magnesium atoms. The results obtained are compared with the available experimental data and the results of other theoretical works.Comment: 30 pages, 10 figures, 3 table

Thermal Density Functional Theory in Context

This chapter introduces thermal density functional theory, starting from the ground-state theory and assuming a background in quantum mechanics and statistical mechanics. We review the foundations of density functional theory (DFT) by illustrating some of its key reformulations. The basics of DFT for thermal ensembles are explained in this context, as are tools useful for analysis and development of approximations. We close by discussing some key ideas relating thermal DFT and the ground state. This review emphasizes thermal DFT's strengths as a consistent and general framework.Comment: Submitted to Spring Verlag as chapter in "Computational Challenges in Warm Dense Matter", F. Graziani et al. ed