Space-time evolution of Dirac wave packets

In this work we study the dynamics of free 3D relativistic Gaussian wave packets with different spin polarization. We analyze the connection between the symmetry of initial state and the dynamical characteristics of moving particle. The corresponding solutions of Dirac equation having different types of symmetry were evaluated analytically and numerically and after that the electron probability densities, as well as, the spin densities were visualized. The average values of velocity of the packet center and the average spin were calculated analytically, and the parameters of transient Zitterbewegung in different directions were obtained. These results can be useful for the interpretation of future experiments with trapped ions.Comment: 10 pages, 7 figure

Spectral methods for the wave equation in second-order form

Current spectral simulations of Einstein's equations require writing the equations in first-order form, potentially introducing instabilities and inefficiencies. We present a new penalty method for pseudo-spectral evolutions of second order in space wave equations. The penalties are constructed as functions of Legendre polynomials and are added to the equations of motion everywhere, not only on the boundaries. Using energy methods, we prove semi-discrete stability of the new method for the scalar wave equation in flat space and show how it can be applied to the scalar wave on a curved background. Numerical results demonstrating stability and convergence for multi-domain second-order scalar wave evolutions are also presented. This work provides a foundation for treating Einstein's equations directly in second-order form by spectral methods.Comment: 16 pages, 5 figure

Would You Choose to be Happy? Tradeoffs Between Happiness and the Other Dimensions of Life in a Large Population Survey

A large literature documents the correlates and causes of subjective well-being, or happiness. But few studies have investigated whether people choose happiness. Is happiness all that people want from life, or are they willing to sacrifice it for other attributes, such as income and health? Tackling this question has largely been the preserve of philosophers. In this article, we find out just how much happiness matters to ordinary citizens. Our sample consists of nearly 13,000 members of the UK and US general populations. We ask them to choose between, and make judgments over, lives that are high (or low) in different types of happiness and low (or high) in income, physical health, family, career success, or education. We find that people by and large choose the life that is highest in happiness but health is by far the most important other concern, with considerable numbers of people choosing to be healthy rather than happy. We discuss some possible reasons for this preference

Quantum phase transitions in disordered dimerized quantum spin models and the Harris criterion

We use quantum Monte Carlo simulations to study effects of disorder on the quantum phase transition occurring versus the ratio g=J/J' in square-lattice dimerized S=1/2 Heisenberg antiferromagnets with intra- and inter-dimer couplings J and J'. The dimers are either randomly distributed (as in the classical dimer model), or come in parallel pairs with horizontal or vertical orientation. In both cases the transition violates the Harris criterion, according to which the correlation-length exponent should satisfy nu >= 1. We do not detect any deviations from the three-dimensional O(3) universality class obtaining in the absence of disorder (where nu = 0.71). We discuss special circumstances which allow nu<1 for the type of disorder considered here.Comment: 4+ pages, 3 figure

Observation of Parity Nonconservation in Møller Scattering

We report a measurement of the parity-violating asymmetry in fixed target electron-electron (Møller) scattering: A_(PV) = [-175 ± 30(stat)± 20(syst)] X 10^(-9). This first direct observation of parity nonconservation in Møller scattering leads to a measurement of the electron’s weak charge at low energy Q^e_W = -0:053 ± 0:011. This is consistent with the standard model expectation at the current level of precision: sin^2θ_W = (M_Z)_(MS) = 0:2293 ± 0:0024(stat) ± 0:0016(syst) ± 0:0006(theory)

Mira's wind explored in scattering infrared CO lines

We have observed the intermediate regions of the circumstellar envelope of Mira (o Ceti) in photospheric light scattered by three vibration-rotation transitions of the fundamental band of CO, from low-excited rotational levels of the ground vibrational state, at an angular distance of beta = 2"-7" away from the star. The data were obtained with the Phoenix spectrometer mounted on the 4 m Mayall telescope at Kitt Peak. The spatial resolution is approximately 0.5" and seeing limited. Our observations provide absolute fluxes, leading to an independent new estimate of the mass-loss rate of approximately 3e-7 Msun/yr, as derived from a simple analytic wind model. We find that the scattered intensity from the wind of Mira for 2" < beta < 7" decreases as beta^-3, which suggests a time constant mass-loss rate, when averaged over 100 years, over the past 1200 years.Comment: accepted for publication in the Astrophysical Journa

Contributions to the Nearby Stars (NStars) Project: Spectroscopy of Stars Earlier than M0 within 40 parsecs: The Northern Sample I

We have embarked on a project, under the aegis of the Nearby Stars (NStars)/ Space Interferometry Mission Preparatory Science Program to obtain spectra, spectral types, and, where feasible, basic physical parameters for the 3600 dwarf and giant stars earlier than M0 within 40 parsecs of the sun. In this paper we report on the results of this project for the first 664 stars in the northern hemisphere. These results include precise, homogeneous spectral types, basic physical parameters (including the effective temperature, surface gravity and the overall metallicity, [M/H]) and measures of the chromospheric activity of our program stars. Observed and derived data presented in this paper are also available on the project's website at http://stellar.phys.appstate.edu/

Neutron-Capture Elements in the Early Galaxy: Insights from a Large Sample of Metal-Poor Giants

New abundances for neutron-capture (n-capture) elements in a large sample of metal-poor giants from the Bond survey are presented. The spectra were acquired with the KPNO 4-m echelle and coude feed spectrographs, and have been analyzed using LTE fine-analysis techniques with both line analysis and spectral synthesis. Abundances of eight n-capture elements (Sr, Y, Zr, Ba, La, Nd, Eu, Dy) in 43 stars have been derived from blue (lambda = 4070--4710, R~20,000, S/N ratio~100-200) echelle spectra and red (lambda = 6100--6180, R~22,000, S/N ratio~100-200) coude spectra, and the abundance of Ba only has been derived from the red spectra for an additional 27 stars. Overall, the abundances show clear evidence for a large star-to-star dispersion in the heavy element-to-iron ratios. The new data also confirm that at metallicities [Fe/H] <~ --2.4, the abundance pattern of the heavy (Z >= 56) n-capture elements in most giants is well-matched to a scaled Solar System r-process nucleosynthesis pattern. The onset of the main r-process can be seen at [Fe/H] ~ --2.9. Contributions from the s-process can first be seen in some stars with metallicities as low as [Fe/H] ~ --2.75, and are present in most stars with metallicities [Fe/H] > --2.3. The lighter n-capture elements (Sr-Y-Zr) are enhanced relative to the heavier r-process element abundances. Their production cannot be attributed solely to any combination of the Solar System r- and main s-processes, but requires a mixture of material from the r-process and from an additional n-capture process which can operate at early Galactic time.Comment: Text + 5 Tables and 11 Figures: Submitted to the Astrophysical Journa

The resultant on compact Riemann surfaces

We introduce a notion of resultant of two meromorphic functions on a compact Riemann surface and demonstrate its usefulness in several respects. For example, we exhibit several integral formulas for the resultant, relate it to potential theory and give explicit formulas for the algebraic dependence between two meromorphic functions on a compact Riemann surface. As a particular application, the exponential transform of a quadrature domain in the complex plane is expressed in terms of the resultant of two meromorphic functions on the Schottky double of the domain.Comment: 44 page

Optimal Constraint Projection for Hyperbolic Evolution Systems

Techniques are developed for projecting the solutions of symmetric hyperbolic evolution systems onto the constraint submanifold (the constraint-satisfying subset of the dynamical field space). These optimal projections map a field configuration to the ``nearest'' configuration in the constraint submanifold, where distances between configurations are measured with the natural metric on the space of dynamical fields. The construction and use of these projections is illustrated for a new representation of the scalar field equation that exhibits both bulk and boundary generated constraint violations. Numerical simulations on a black-hole background show that bulk constraint violations cannot be controlled by constraint-preserving boundary conditions alone, but are effectively controlled by constraint projection. Simulations also show that constraint violations entering through boundaries cannot be controlled by constraint projection alone, but are controlled by constraint-preserving boundary conditions. Numerical solutions to the pathological scalar field system are shown to converge to solutions of a standard representation of the scalar field equation when constraint projection and constraint-preserving boundary conditions are used together.Comment: final version with minor changes; 16 pages, 14 figure