Birkhoff Theorem and Matter

Birkhoff's theorem for spherically symmetric vacuum spacetimes is a key theorem in studying local systems in general relativity theory. However realistic local systems are only approximately spherically symmetric and only approximately vacuum. In a previous paper, we showed the theorem remains approximately true in an approximately spherically symmetric vacuum space time. In this paper we prove the converse case: the theorem remains approximately true in a spherically symmetric, approximately vacuum space time.Comment: 7 pages, Revtex

Ideal Stars and General Relativity

We study a system of differential equations that governs the distribution of matter in the theory of General Relativity. The new element in this paper is the use of a dynamical action principle that includes all the degrees of freedom, matter as well as metric. The matter lagrangian defines a relativistic version of non-viscous, isentropic hydrodynamics. The matter fields are a scalar density and a velocity potential; the conventional, four-vector velocity field is replaced by the gradient of the potential and its scale is fixed by one of the eulerian equations of motion, an innovation that significantly affects the imposition of boundary conditions. If the density is integrable at infinity, then the metric approaches the Schwarzschild metric at large distances. There are stars without boundary and with finite total mass; the metric shows rapid variation in the neighbourhood of the Schwarzschild radius and there is a very small core where a singularity indicates that the gas laws break down. For stars with boundary there emerges a new, critical relation between the radius and the gravitational mass, a consequence of the stronger boundary conditions. Tentative applications are suggested, to certain Red Giants, and to neutron stars, but the investigation reported here was limited to polytropic equations of state. Comparison with the results of Oppenheimer and Volkoff on neutron cores shows a close agreement of numerical results. However, in the model the boundary of the star is fixed uniquely by the required matching of the interior metric to the external Schwarzschild metric, which is not the case in the traditional approach.Comment: 26 pages, 7 figure

Current-Induced Effects in Nanoscale Conductors

We present an overview of current-induced effects in nanoscale conductors with emphasis on their description at the atomic level. In particular, we discuss steady-state current fluctuations, current-induced forces, inelastic scattering and local heating. All of these properties are calculated in terms of single-particle wavefunctions computed using a scattering approach within the static density-functional theory of many-electron systems. Examples of current-induced effects in atomic and molecular wires will be given and comparison with experimental results will be provided when available.Comment: revtex, 10 pages, 8 figure

On the Truncated Pareto Distribution with applications

The Pareto probability distribution is widely applied in different fields such us finance, physics, hydrology, geology and astronomy. This note deals with an application of the Pareto distribution to astrophysics and more precisely to the statistical analysis of mass of stars and of diameters of asteroids. In particular a comparison between the usual Pareto distribution and its truncated version is presented. Finally a possible physical mechanism that produces Pareto tails for the distribution of the masses of stars is suggested.Comment: 10 pages 6 figure

New Jacobi-Like Identities for Z_k Parafermion Characters

We state and prove various new identities involving the Z_K parafermion characters (or level-K string functions) for the cases K=4, K=8, and K=16. These identities fall into three classes: identities in the first class are generalizations of the famous Jacobi theta-function identity (which is the K=2 special case), identities in another class relate the level K>2 characters to the Dedekind eta-function, and identities in a third class relate the K>2 characters to the Jacobi theta-functions. These identities play a crucial role in the interpretation of fractional superstring spectra by indicating spacetime supersymmetry and aiding in the identification of the spacetime spin and statistics of fractional superstring states.Comment: 72 pages (or 78/2 = 39 pages in reduced format

iPhone or Kindle: Competition of Electronic Books Sales

With the technical development of the reading equipment, e-books have witnessed a gradual and steady increase in sales in recent years. Last year, smart phones announced to be able to perform additional functions as e-book reading devices, making it possible for retailers selling e-books for smart phones (SPR) such as iPhone to differentiate with those selling e-books for specific reading equipment (SER) such as Amazon Kindle. We develop a game theory model to examine the competition between SER and SPR retailers. We derive the equilibrium price and analyze the factors that affect equilibrium outcomes under both scenarios of complete and incomplete information. Our results suggest that reduced cost due to inconvenience of reading e-books over iPhone lowers equilibrium prices, and reduced cost of specific reading equipment leads to more intense price competition. Under information asymmetry, we show that SER retailers will increase the price at equilibrium

Variant supercurrents and Noether procedure

Consistent supercurrent multiplets are naturally associated with linearized off-shell supergravity models. In arXiv:1002.4932 we presented the hierarchy of such supercurrents which correspond to all the models for linearized 4D N = 1 supergravity classified a few years ago. Here we analyze the correspondence between the most general supercurrent given in arXiv:1002.4932 and the one obtained eight years ago in hep-th/0110131 using the superfield Noether procedure. We apply the Noether procedure to the general N = 1 supersymmetric nonlinear sigma-model and show that it naturally leads to the so-called S-multiplet, revitalized in arXiv:1002.2228.Comment: 6 page

Predicted modulated differential rates for direct WIMP searches at low energy transfers

The differential event rate for direct detection of dark matter, both the time averaged and the modulated one due to the motion of the Earth, are discussed. The calculations focus on relatively light cold dark matter candidates (WIMP) and low energy transfers. It is shown that for sufficiently light WIMPs the extraction of relatively large nucleon cross sections is possible. Furthermore for some WIMP masses the modulation amplitude may change sign, meaning that, in such a case, the maximum rate may occur six months later than naively expected. This effect can be exploited to yield information about the mass of the dark matter candidate, if and when the observation of the modulation of the event rate is established.Comment: 16 pages, 22 figures; references adde

On the spherical-axial transition in supernova remnants

A new law of motion for supernova remnant (SNR) which introduces the quantity of swept matter in the thin layer approximation is introduced. This new law of motion is tested on 10 years observations of SN1993J. The introduction of an exponential gradient in the surrounding medium allows to model an aspherical expansion. A weakly asymmetric SNR, SN1006, and a strongly asymmetric SNR, SN1987a, are modeled. In the case of SN1987a the three observed rings are simulated.Comment: 19 figures and 14 pages Accepted for publication in Astrophysics & Space Science in the year 201

Investigation of conduction band structure, electron scattering mechanisms and phase transitions in indium selenide by means of transport measurements under pressure

In this work we report on Hall effect, resistivity and thermopower measurements in n-type indium selenide at room temperature under either hydrostatic and quasi-hydrostatic pressure. Up to 40 kbar (= 4 GPa), the decrease of carrier concentration as the pressure increases is explained through the existence of a subsidiary minimum in the conduction band. This minimum shifts towards lower energies under pressure, with a pressure coefficient of about -105 meV/GPa, and its related impurity level traps electrons as it reaches the band gap and approaches the Fermi level. The pressure value at which the electron trapping starts is shown to depend on the electron concentration at ambient pressure and the dimensionality of the electron gas. At low pressures the electron mobility increases under pressure for both 3D and 2D electrons, the increase rate being higher for 2D electrons, which is shown to be coherent with previous scattering mechanisms models. The phase transition from the semiconductor layered phase to the metallic sodium cloride phase is observed as a drop in resistivity around 105 kbar, but above 40 kbar a sharp nonreversible increase of the carrier concentration is observed, which is attributed to the formation of donor defects as precursors of the phase transition.Comment: 18 pages, Latex, 10 postscript figure