Homotopy Approach to Quantum Gravity

Gravity may be a quantum-space-time effect. General relativity is quantized by small generic changes in its commutation relations that make its Lie algebras simple on all levels, positing extra variables frozen by self-organization as needed. This quantizes space-time coordinates as well as fields and eliminates physical singularities. Fermi statistics and sl (nℝ) Lie algebras are assumed for all levels. Spin 1/2 is taken to be anomalous, arising from vacuum organization; the spin-statistics relation is incorporated. The gravitational field is quartic in Fermi variables. Einstein’s non-commutativity of parallel transport emerges as a vestige of Heisenberg’s quantum non-commutativity near the classical limit.     

Exact analytical solutions for shallow impurity states in symmetrical paraboloidal and hemiparaboloidal quantum dots

The problem of a shallow donor impurity located at the centre of a symmetrical paraboloidal quantum dot (SPQD) is solved exactly. The Schrödinger equation is separated in the paraboloidal coordinate system. Three different cases are discussed for the radial-like equations. For a bound donor, the energy is negative and the solutions are described by Whittaker functions. For a non-bound donor, the energy is positive and the solutions become coulomb wave functions. In the last case, the energy is equal to zero and the solutions reduce to Bessel functions. Using the boundary conditions at the dot surfaces, the variations of the donor kinetic and potential energies versus the size of the dot are obtained. The problem of a shallow donor impurity in a Hemiparaboloidal Quantum dot (HPQD) is also studied. It is shown that the wave functions of a HPQD are specific linear combinations of those of a SPQD.     

Fe-B-Y-Nb bulk metallic glasses in relation to clusters

Bulk metallic glass formations in the Fe-B-Y-Nb quaternary alloy system were investigated by using the cluster line rule in combination with the minor alloying principle. The Fe-B-Y ternary system was selected as the basic system and the intersections of cluster lines were taken as the basic ternary compositions. The basic compositions were further alloyed with minor amounts of Nb. After 3–5 at.% Nb was added, the basic composition Fe_68.6B_25.7Y_5.7, which was developed from the most densely packed cluster Fe₈B₃, formed 3 mm bulk metallic glasses. These quaternary bulk metallic glasses (Fe_68.6B_25.7Y_5.7)_100−x Nb _x (x = 3–5 at.%) are expressed approximately with a unified simple composition formula: (Fe₈B₃)₁(Y, Nb)₁. The (Fe_68.6B_25.7Y_5.7)₉₇Nb₃ bulk metallic glass has the largest glass forming ability with the following characteristic parameters T _g = 907 K, T _x = 1006 K, T _g/T _l = 0.644, γ = 0.434, and longness t = 22 mm. The combination of the cluster line rule and the minor-alloying principle is a promising new route towards the quantitative composition design of multi-component metallic glasses. Supported by the National Natural Science Foundation of China (Grant Nos. 50671018, 50631010 and 50401020) and the National Basic Research Program of China (Grant No. 2007CB613902)     

First-Order Intertwining Operators with Position Dependent Mass and <Emphasis Type="Italic">η</Emphasis>-Weak-Pseudo-Hermiticity Generators

A Hermitian and an anti-Hermitian first-order intertwining operators are introduced and a class of η-weak-pseudo-Hermitian position-dependent mass (PDM) Hamiltonians are constructed. A corresponding reference-target η-weak-pseudo-Hermitian PDM—Hamiltonians’ map is suggested. Some η-weak-pseudo-Hermitian -symmetric Scarf II and periodic-type models are used as illustrative examples. Energy-levels crossing and flown-away states phenomena are reported for the resulting Scarf II spectrum. Some of the corresponding η-weak-pseudo-Hermitian Scarf II- and periodic-type-isospectral models ( -symmetric and non- -symmetric) are given as products of the reference-target map.     

Weyl’s Type Estimates on the Eigenvalues of Critical Schrödinger Operators

We consider on a bounded domain \(\Omega \subset {\mathbb{R}}^N\) , the Schrödinger operator ? Δ ? V supplemented with Dirichlet boundary solutions. The potential V is either the critical inverse square potential V(x) = (N ? 2)²/4|x|^?2 or the critical borderline potential V(x) =  (1/4)dist(x, ?Ω)^?2. We present explicit asymptotic estimates on the eigenvalues of the critical Schrödinger operator in each case, based on recent results on improved Hardy–Sobolev type inequalities.     

Fluorescence Spectral Properties of Rhodamine 6G at the Silica/Water Interface

In this work, total internal reflection synchronous fluorescence spectroscopy (TIRSF) is applied successfully to investigate rhodamine 6G (R6G) at the silica/water interface. In comparison with the bulk spectra, 5 nm red shift is observed in the interface spectra, which is mainly due to the limitation of freedom of rotational movement of R6G molecules at the interface. The increase of R6G concentration induces the self-quenching of adsorbate at the interface. The dependence of interfacial fluorescence on the acidity and ionic strength was studied. Both the acidity and ionic strength affect the adsorptive behaviors of R6G at the silica/water interface.     

Fluorescence Dynamics of Three UV-B Sunscreens

Polarity of the surrounding medium affects the excited states of UV-B sunscreens. Therefore understanding excited state processes in a mixed polarity model system similar to skin is essential. We report the excited state lifetimes, quantum yields, radiative and non-radiative rates of three sunscreens. Among the three UV-B sunscreens studied, octyl salicylate emits from a single excited state, while padimate O and octyl methoxy cinnamate show multiple states. The radiative rates of salicylate and cinnamate are approximately constant, while that of padimate O depends strongly on solvent. The non-radiative rates of all sunscreens vary with solvent polarity. Compared to salicylate and cinnamate, padimate O is complex to analyze because of its two emission peaks and one peak’s strong dependence on the dielectric constant. High absorbance, broad absorption peak with small fluorescence quantum yield, and low radiative rate make octyl methoxy cinnamate a superior UV-B sunscreen ingredient. The complexity in excited-state analysis shows that the lifetimes of the sunscreens are critical parameters, in addition to absorbance and quantum yield. Fluorescence lifetime substantiates the use of polystyrene nanospheres as a model host to study the photo-physical properties of sunscreen in a heterogeneous environment.     

Quantum tunneling and quasinormal modes in the spacetime of the Alcubierre warp drive

In a seminal paper, Alcubierre showed that Einstein’s theory of general relativity appears to allow a super-luminal motion. In the present study, we use a recent eternal-warp-drive solution found by Alcubierre to study the effect of Hawking radiation upon an observer located within the warp drive in the framework of the quantum tunneling method. We find the same expression for the Hawking temperatures associated with the tunneling of both massive vector and scalar particles, and show this expression to be proportional to the velocity of the warp drive. On the other hand, since the discovery of gravitational waves, the quasinormal modes (QNMs) of black holes have also been extensively studied. With this purpose in mind, we perform a QNM analysis of massive scalar field perturbations in the background of the eternal-Alcubierre-warp-drive spacetime. Our analytical analysis shows that massive scalar perturbations lead to stable QNMs.     

Strong lensing of a regular black hole with an electrodynamics source

In this paper we have investigated the gravitational lensing phenomenon in the strong field regime for a regular, charged, static black holes with non-linear electrodynamics source. We have obtained the angle of deflection and compared it to a Schwarzschild black hole and Reissner Nordström black hole with similar properties. We have also done a graphical study of the relativistic image positions and magnifications. We hope that this method may be useful in the detection of non-luminous bodies like this current black hole.     

The shadow of a collapsing dark star

The shadow of a black hole is usually calculated, either analytically or numerically, on the assumption that the black hole is eternal, i.e., that it has existed for all time. Here we ask the question of how this shadow comes about in the course of time when a black hole is formed by gravitational collapse. To that end we consider a star that is spherically symmetric, dark and non-transparent and we assume that it begins, at some instant of time, to collapse in free fall like a ball of dust. We analytically calculate the dependence on time of the angular radius of the shadow, first for a static observer who is watching the collapse from a certain distance and then for an observer who is falling towards the centre following the collapsing star.