Eikonal Approximation to 5D Wave Equations as Geodesic Motion in a Curved 4D Spacetime

We first derive the relation between the eikonal approximation to the Maxwell wave equations in an inhomogeneous anisotropic medium and geodesic motion in a three dimensional Riemannian manifold using a method which identifies the symplectic structure of the corresponding mechanics. We then apply an analogous method to the five dimensional generalization of Maxwell theory required by the gauge invariance of Stueckelberg's covariant classical and quantum dynamics to demonstrate, in the eikonal approximation, the existence of geodesic motion for the flow of mass in a four dimensional pseudo-Riemannian manifold. These results provide a foundation for the geometrical optics of the five dimensional radiation theory and establish a model in which there is mass flow along geodesics. Finally we discuss the case of relativistic quantum theory in an anisotropic medium as well. In this case the eikonal approximation to the relativistic quantum mechanical current coincides with the geodesic flow governed by the pseudo-Riemannian metric obtained from the eikonal approximation to solutions of the Stueckelberg-Schr\"odinger equation. This construction provides a model for an underlying quantum mechanical structure for classical dynamical motion along geodesics on a pseudo-Riemannian manifold. The locally symplectic structure which emerges is that of Stueckelberg's covariant mechanics on this manifold.Comment: TeX file. 17 pages. Rewritten for clarit

Casimir forces in Bose-Einstein condensates: finite size effects in three-dimensional rectangular cavities

The Casimir force due to {\it thermal} fluctuations (or pseudo-Casimir force) was previously calculated for the perfect Bose gas in the slab geometry for various boundary conditions. The Casimir pressure due to {\it quantum} fluctuations in a weakly-interacting dilute Bose-Einstein condensate (BEC) confined to a parallel plate geometry was recently calculated for Dirichlet boundary conditions. In this paper we calculate the Casimir energy and pressure due to quantum fluctuations in a zero-temperature homogeneous weakly-interacting dilute BEC confined to a parallel plate geometry with periodic boundary conditions and include higher-order corrections which we refer to as Bogoliubov corrections. The leading order term is identified as the Casimir energy of a massless scalar field moving with wave velocity equal to the speed of sound in the BEC. We then obtain the leading order Casimir pressure in a general three-dimensional rectangular cavity of arbitrary lengths and obtain the finite-size correction to the parallel plate scenario.Comment: 12 pages; no figures; v.2: version accepted for publication in JSTAT v.3: references adde

G-CORE a core for future graph query languages

We report on a community effort between industry and academia to shape the future of graph query languages. We argue that existing graph database management systems should consider supporting a query language with two key characteristics. First, it should be composable, meaning, that graphs are the input and the output of queries. Second, the graph query language should treat paths as first-class citizens. Our result is G-CORE, a powerful graph query language design that fulfills these goals, and strikes a careful balance between path query expressivity and evaluation complexity

Employment generation by small firms in Spain

Despite the relevance in terms of policy, we still know little in Spain about where and by whom jobs are created, and how that is affecting the size distribution of firms. The main innovation of this paper is to use a rich database that overcomes the problems encountered by other firm-level studies to shed some light on the employment generation of small firms in Spain. We find that small firms contribute to employment disproportionately across all sectors of the economy although the difference between their employment and job creation share is largest in the manufacturing sector. The job creators in that sector are both new and established firms whereas only new small firms outperform their larger counterparts in the service sector. The large annual job creation of the small firm size class is shifting the firm size distribution towards the very small production units, although not uniformly across industries of different technology intensit

The labor market effects of technology shocks

We analyze the effects of neutral and investment-specific technology shocks on hours worked and unemployment. We characterize the response of unemployment in terms of job separation and job finding rates. We find that job separation rates mainly account for the impact response of unemployment while job finding rates for movements along its adjustment path. Neutral shocks increase unemployment and explain a substantial portion of unemployment and output volatilityinvestment-specific shocks expand employment and hours worked and mostly contribute to hours worked volatility. We show that this evidence is consistent with the view that neutral technological progress prompts Schumpeterian creative destruction, while investment specific technological progress has standard neoclassical feature

Wage inequality, segregation by skill and the price of capital in an assignment model

Some pieces of empirical evidence suggest that in the U.S., over the last few decades, (i) wage inequality between-plants has risen much more than wage inequality within-plants and (ii) there has been an increase in the segregation of workers by skill into separate plants. This paper presents a frictionless assignment model in which these two features can be explained simultaneously as the result of the decline in the relative price of capital. Additional implications of the model regarding the skill premium and the dispersion in labor productivity across plants are also consistent with the empirical evidence. [resumen de autor