Quantum-Gravitational Diffusion and Stochastic Fluctuations in the Velocity of Light

We argue that quantum-gravitational fluctuations in the space-time background give the vacuum non-trivial optical properties that include diffusion and consequent uncertainties in the arrival times of photons, causing stochastic fluctuations in the velocity of light in vacuo. Our proposal is motivated within a Liouville string formulation of quantum gravity that also suggests a frequency-dependent refractive index of the particle vacuum. We construct an explicit realization by treating photon propagation through quantum excitations of D-brane fluctuations in the space-time foam. These are described by higher-genus string effects, that lead to stochastic fluctuations in couplings, and hence in the velocity of light. We discuss the possibilities of constraining or measuring photon diffusion in vacuo via -ray observations of distant astrophysical sources.     

Stringy space–time foam,Finsler-like metrics and dark matter relics

We discuss modifications of the thermal dark matter (DM) relic abundances in stringy cosmologies with D-particle space–time foamy backgrounds. As a result of back-reaction of massive DM on the background space–time, owing to its interaction with D-particle defects in the foam, quantum fluctuations are induced in the space–time metric. We demonstrate that these lead to the presence of extra source terms in the Boltzmann equation used to determine the thermal dark matter relic abundances. The source terms are determined by the specific form of the induced metric deformations; the latter depend on the momentum transfer of the DM particle during its interactions with the D-particle defects and so are akin to Finsler metrics. In the case of low string scales, arising from large extra dimensions, our results may have phenomenological implications for the search of viable supersymmetric models.     

Optical band gap and optical constants in a-Se80Te20−xPbx thin films

The optical constants (absorption coefficient, refractive index, extention coefficient, real and imaginary part of dielectric constant) have been studied for a-Se₈₀Te_20−xPb_x (where x = 0, 2, 6, 10) thin films as a function of photon energy in the wave length range (500–1000 nm). It has been found that the optical band gap increases while the refractive index and the extinction coefficient (k) decreases on incorporation of lead in Se–Te system. The value of absorption coefficient (α) and the extinction coefficient (k) increases, while the value of refractive index (n) decreases with incident photon energy. The results are interpreted in terms of the change in concentration of localized states due to the shift in fermi level.     

Generally Covariant Schrödinger Equation in Newton–Cartan Space–Time. Part II

Schrödinger equation in Newton–Cartan space–time can be obtained from Einstein equivalence principle, that is firstly one should obtain generally covariant Schrödinger's equation in Galilean space–time (using generally covariant Hamilton–Jacobi formalism and Schrödinger's Ansatz, as was previously shown) and get Schrödinger's equation in Newton–Cartan space–time with the help of equivalence principle. The equation possesses a gauge freedom f connected with phase transformation of the wave function. But absolute elements of the space–time possess a symmetry group and they depend on f. So, a natural problem arises: to find the gauge f in which absolute elements become invariant with respect to the group. In the paper the gauge f is found with the help of space–time properties, that is transformation rule of the wave function is obtained from the space–time structure (in Newton–Cartan space–time). The special form of f is found in the case when the space–time as a whole possesses a symmetry.     

Optical properties of ZnTe films

Optical properties of p-type ZnTe films, deposited by hot-wall vacuum evaporation, were studied extensively in the range of incident photon energy 0.6–2.6 eV. Variations of refractive index, absorption and extinction coefficients with incident photon energy are reported in this communication.     

The incompressible Navier–Stokes equations from black hole membrane dynamics

We consider the dynamics of a d+1 space–time dimensional membrane defined by the event horizon of a black brane in (d+2)-dimensional asymptotically Anti-de Sitter space–time and show that it is described by the d-dimensional incompressible Navier–Stokes equations of non-relativistic fluids. The fluid velocity corresponds to the normal to the horizon while the rate of change in the fluid energy is equal to minus the rate of change in the horizon cross-sectional area. The analysis is performed in the Membrane Paradigm approach to black holes and it holds for a general non-singular null hypersurface, provided a large scale hydrodynamic limit exists. Thus we find, for instance, that the dynamics of the Rindler acceleration horizon is also described by the incompressible Navier–Stokes equations. The result resembles the relation between the Burgers and KPZ equations and we discuss its implications.     

Spinor-vector duality in heterotic string vacua

Classification of the N=1 space–time supersymmetric fermionic Z₂×Z₂ heterotic-string vacua with symmetric internal shifts, revealed a novel spinor-vector duality symmetry over the entire space of vacua, where the S_t↔V duality interchanges the spinor plus anti-spinor representations with vector representations. In this paper we demonstrate that the spinor-vector duality exists also in fermionic Z₂ heterotic string models, which preserve N=2 space–time supersymmetry. In this case the interchange is between spinorial and vectorial representations of the unbroken SO(12) GUT symmetry. We provide a general algebraic proof for the existence of the S_t↔V duality map. We present a novel basis to generate the free fermionic models in which the ten-dimensional gauge degrees of freedom are grouped into four groups of four, each generating an SO(8) modular block. In the new basis the GUT symmetries are produced by generators arising from the trivial and non-trivial sectors, and due to the triality property of the SO(8) representations. Thus, while in the new basis the appearance of GUT symmetries is more cumbersome, it may be more instrumental in revealing the duality symmetries that underly the string vacua.     

Dirac Equation in Space–Time with Torsion

The Dirac equation in a curved space–time endowed with compatible affine connection is reconsidered. After a detailed decomposition of the total action, the equation is obtained by varying with respect to the Dirac spinor and the torsion field. The result is a known Dirac-like equation with constraints that can be interpreted as the equation of a self-interacting spin 1/2 particle in curved space–time. The scheme is then translated into the language of the 2-spinor formalism of curved space–time based on the choice of a null tetrad frame. The spinorial equation so obtained coincides with the standard one in case of no torsion, while in general it remains a nonlinear equation describing a self-interacting spin 1/2 particle. The nonlinearity is produced by the interaction of the particle with its own current that remains conserved as in the free torsion case.     

Anatomy of a confining string

We review recent papers on the anatomy of the confining string in the Abelian Higgs model with condensed Higgs field. The basic observation is that apart from the well known Abrikosov–Nielsen–Olesen strings of finite transverse size there exist infinitely thin topological strings. These mathematically thin strings are responsible, in particular, for a stringy correction to the potential between confined charges at short distances. Possible implications for QCD are briefly discussed.     

Coulomb scattering for scalar field in Schrödinger picture

The scattering of a charged scalar field on Coulomb potential on de Sitter space–time is studied using the solution of the free Klein–Gordon equation. We find that the scattering amplitude is independent of the choice of the picture and in addition the total energy is conserved in the scattering process.     

e − e + Production by a Nambu string

We analytically calculate the probability ofe ^– e ⁺ production with a given relative energy from a closed string arising from the Nambu action as a solution of a circularly oscillating string as, perhaps, the simplest generalization of the classic pointlike particle. A numerical analysis of the result is also given.     

On Waylen's Regular Axisymmetric Similarity Solutions

We review the similarity solutions proposed by Waylen for a regular time–dependent axisymmetric vacuum space–time, and show that the key equation introduced to solve the invariant surface conditions is related by a Bäcklund transform to a restriction on the similarity variables. We further show that the vacuum space–times produced via this path automatically possess a (possibly homothetic) Killing vector, which may be time–like.     

Interacting Gravitational and Dirac Fields with Torsion

A general interaction scheme is formulated in a general space–time with torsion from the action principle by considering the gravitational, the Dirac, and the torsion field as independent fields. Some components of the torsion field come out to be automatically zero. Both the resulting Einstein-like and the Dirac-like fields equations contain nonlinear terms given by a self-interaction of the Dirac spinor and originally produced by torsion. The theory is specialized to the Robertson–Walker space–time without torsion. To solve he corresponding equations, that still have a complex structure, the spin coefficients have to be calculated explicitly from the tetrad employed. A solution, even if simple and elementary, is then determined.     

Vacuum quantum effect for curved boundaries in static Robertson–Walker space–time

The energy–momentum tensor for a massless conformally coupled scalar field in the region between two curved boundaries in k=−1 static Robertson–Walker space–time is investigated. We assume that the scalar field satisfies the Dirichlet boundary condition on the boundaries. k=−1 Robertson–Walker space is conformally related to the Rindler space, as a result we can obtain vacuum expectation values of energy–momentum tensor for conformally invariant field in Robertson–Walker space from the corresponding Rindler counterpart by the conformal transformation.     

Nongeneric SUSY in Spinning NUT–Kerr–Newman Space–Time

The supersymmetric extension of theNUT–Kerr–Newman (NUT–KN)space–time is investigated. Along with fourstandard supersymmetries, this type of space–timeadmits fermionic symmetry generated by the square root of the bosonic constant of motion exceptthe Hamiltonian. Such a new supersymmetry corresponds tothe Killing–Yano tensor, which plays an importantrole in solving various field equations in thisspace–time.     

Dirac Equation with Central Potential: Discrete Spectrum of the Hydrogen Atom in the Robertson–Walker Space–Time

The formulation of the Dirac equation withelectromagnetic field for a general space–time isspecialized to the Robertson–Walker metric. For aclass of physically meaningful electromagneticpotentials the angular part of the wave function separates asin the free-field case. The scheme is explicitly studiedfor a Coulomb potential. By using a realisticapproximation method one recovers the discrete energy levels of the hydrogen atom in Minkowski space.In case of static space–time, the result is exactfor zero curvature, while it is approximate for nonzerocurvature. The very good order of accuracy of the result is established by a comparison withsimilar qualitative and perturbative results.     

Black Hole and Cosmic Entropy for Schwarzschild–de Sitter Space–Time

We calculate the free energy and the entropy of a scalar field in terms of the brick-wall method in the background of the Schwarzschild–de Sitter space–time. We obtain the entropy of a black hole and the cosmic entropy at nonasymptotic flat space. When the cut-off satisfies the proper condition, the entropy of a black hole is proportional to the area of a black hole horizon, and the cosmic entropy is proportional to the cosmic horizon area.     

Spectral dependence of transient reflectance in a ZnO epitaxial film at room temperature

We demonstrated the spectral dependence of time-resolved reflectance in a ZnO epitaxial film at room temperature. The ultrafast thermalization time increases as increasing the excitation photon energy accompanied with the hot phonon effect. The obtained recovery time of renormalized bandgap, associated with the nonradiative decay or the free exciton formation, is independent of photon energy. Based on a theoretical model to calculate the carrier-induced change of refractive index in ZnO, the spectral dependent transient reflectance can be successfully analyzed as a result of combined effects of band-filling (BF) and bandgap renormalization (BGR). The measured transient reflectance decreases with decreasing the photon energy for excitation above the bandgap states revealing the significance of competition of the BF and BGR effects.     

Effect of cadmium addition on the optical constants of thermally evaporated amorphous Se–S–Cd thin films

Se₇₅S_25−xCd_x is a promising ternary material, which has received considerable attention due to its applications in the fabrication of various solid state devices. These have distinct advantages, large packing density, mass replication, fast data rate, high signal-to-noise ratio and high immunity to defects. Measurements of optical constants (absorption coefficient, refractive index, extinction coefficient, real and imaginary part of the dielectric constant) have been made on Se₇₅S_25−xCd_x (where x = 0, 2, 4, 6 and 8) thin films of thickness 3000 Å as a function of photon energy in the wave length range 400–1000 nm. It has been found that the optical band gap and extinction coefficient increases while the value refractive index decreases on incorporation of cadmium in Se–S system. The results are interpreted in terms of the change in concentration of localized states due to the shift in Fermi level. Due to the large absorption coefficient and compositional dependence of reflectance, these materials may be suitable for optical disk material.