Derivation of the Lindblad Generator Structure by use of the It\^o Stochastic Calculus

We use the It\^o stochastic calculus to give a simple derivation of the Lindblad form for the generator of a completely positive density matrix evolution, by specialization from the corresponding global form for a completely positive map. As a by-product, we obtain a generalized generator for a completely positive stochastic density matrix evolution.Comment: Plain TEX, no figures or table

The Step-Harmonic Potential

We analyze the behavior of a quantum system described by a one-dimensional asymmetric potential consisting of a step plus a harmonic barrier. We solve the eigenvalue equation by the integral representation method, which allows us to classify the independent solutions as equivalence classes of homotopic paths in the complex plane. We then consider the propagation of a wave packet reflected by the harmonic barrier and obtain an expression for the interaction time as a function of the peak energy. For high energies we recover the classical half-period limit.Comment: 19 pages, 7 figure

Do supernovae favor tachyonic Big Brake instead de Sitter?

We investigate whether a tachyonic scalar field, encompassing both dark energy and dark matter-like features will drive our universe towards a Big Brake singularity or a de Sitter expansion. In doing this it is crucial to establish the parameter domain of the model, which is compatible with type Ia supernovae data. We find the 1-sigma contours and evolve the tachyonic sytem into the future. We conclude, that both future evolutions are allowed by observations, Big Brake becoming increasingly likely with the increase of the positive model parameter k.Comment: 8 pages, 6 figures, to be published in the Proceedings of the Invisible Universe International Conference, Paris, 2009, Ed. J. M. Alimi; v2: reference

Spacetime geometries and light trapping in travelling refractive index perturbations

In the framework of transformation optics, we show that the propagation of a locally superluminal refractive index perturbation (RIP) in a Kerr medium can be described, in the eikonal approximation, by means of a stationary metric, which we prove to be of Gordon type. Under suitable hypotheses on the RIP, we obtain a stationary but not static metric, which is characterized by an ergosphere and by a peculiar behaviour of the geodesics, which are studied numerically, also accounting for material dispersion. Finally, the equation to be satisfied by an event horizon is also displayed and briefly discussed.Comment: 14 pages, 7 figure

Observational Constraints on the Generalized Chaplygin Gas

In this paper we study a quintessence cosmological model in which the dark energy component is considered to be the Generalized Chaplygin Gas and the curvature of the three-geometry is taken into account. Two parameters characterize this sort of fluid, the $\nu$ and the $\alpha$ parameters. We use different astronomical data for restricting these parameters. It is shown that the constraint $\nu \lesssim \alpha$ agrees enough well with the astronomical observations.Comment: Accepted by IJMPD; 18 pages; 10 Figure

Inverse Spin Hall Effect and Anomalous Hall Effect in a Two-Dimensional Electron Gas

We study the coupled dynamics of spin and charge currents in a two-dimensional electron gas in the transport diffusive regime. For systems with inversion symmetry there are established relations between the spin Hall effect, the anomalous Hall effect and the inverse spin Hall effect. However, in two-dimensional electron gases of semiconductors like GaAs, inversion symmetry is broken so that the standard arguments do not apply. We demonstrate that in the presence of a Rashba type of spin-orbit coupling (broken structural inversion symmetry) the anomalous Hall effect, the spin Hall and inverse spin Hall effect are substantially different effects. Furthermore we discuss the inverse spin Hall effect for a two-dimensional electron gas with Rashba and Dresselhaus spin-orbit coupling; our results agree with a recent experiment.Comment: 5 page

Reply to Comment on: Hawking radiation from ultrashort laser pulse filaments

A comment by R. Schutzhold et al. raises possible concerns and questions regarding recent measurements of analogue Hawking radiation. We briefly reply to the opinions expressed in the comment and sustain that the origin of the radiation may be understood in terms of Hawking emission

Tachyon cosmology with non-vanishing minimum potential: a unified model

We investigate the tachyon condensation process in the effective theory with non-vanishing minimum potential and its implications to cosmology. It is shown that the tachyon condensation on an unstable three-brane described by this modified tachyon field theory leads to lower-dimensional branes (defects) forming within a stable three-brane. Thus, in the cosmological background, we can get well-behaved tachyon matter after tachyon inflation, (partially) avoiding difficulties encountered in the original tachyon cosmological models. This feature also implies that the tachyon inflated and reheated universe is followed by a Chaplygin gas dark matter and dark energy universe. Hence, such an unstable three-brane behaves quite like our universe, reproducing the key features of the whole evolutionary history of the universe and providing a unified description of inflaton, dark matter and dark energy in a very simple single-scalar field model.Comment: 18 p

Holographic Dark Energy Scenario and Variable Modified Chaplygin Gas

In this letter, we have considered that the universe is filled with normal matter and variable modified Chaplygin gas. Also we have considered the interaction between normal matter and variable modified Chaplygin gas in FRW universe. Then we have considered a correspondence between the holographic dark energy density and interacting variable modified Chaplygin gas energy density. Then we have reconstructed the potential of the scalar field which describes the variable modified Chaplygin cosmology.Comment: 4 latex pages, no figures, RevTeX styl

Dark matter effects in vacuum spacetime

We analyze a toy model describing an empty spacetime in which the motion of a test mass (and the trajectories of photons) evidence the presence of a continuous and homogeneous distribution of matter; however, since the energy-momentum tensor vanishes, no real matter or energy distribution is present at all. Thus, a hypothetical observer will conclude that he is immersed in some sort of dark matter, even though he has no chance to directly detect it. This suggests yet another possibility of explaining the elusive dark matter as a purely dynamical effect due to the curvature of spacetime.Comment: 5 pages, 2 figures, expanded with comments about the exact motion and curvature invariant