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.     

Density perturbation in the models reconstructed from jerk parameter

The present work deals with the late time evolution of the linear density contrast in the dark energy models reconstructed from the jerk parameter. It is found that the non-interacting models are favoured compared to the models where an interaction is allowed in the dark sector.     

Towards the map of quantum gravity

In this paper we point out some possible links between different approaches to quantum gravity and theories of the Planck scale physics. In particular, connections between loop quantum gravity, causal dynamical triangulations, Ho?ava–Lifshitz gravity, asymptotic safety scenario, Quantum Graphity, deformations of relativistic symmetries and nonlinear phase space models are discussed. The main focus is on quantum deformations of the Hypersurface Deformations Algebra and Poincaré algebra, nonlinear structure of phase space, the running dimension of spacetime and nontrivial phase diagram of quantum gravity. We present an attempt to arrange the observed relations in the form of a graph, highlighting different aspects of quantum gravity. The analysis is performed in the spirit of a mind map, which represents the architectural approach to the studied theory, being a natural way to describe the properties of a complex system. We hope that the constructed graphs (maps) will turn out to be helpful in uncovering the global picture of quantum gravity as a particular complex system and serve as a useful guide for the researchers.     

Precise determination of hyperfine interactions and second-order doppler shift in <Superscript>149</Superscript>Sm Mössbauer transition

We have succeeded in precisely determining the hyperfine interactions, particularly the isomer shifts, in the ¹⁴⁹Sm Mössbauer transition. The difference in the nuclear radii between the ground and excited states is critical for the determination of isomer shifts but is relatively small in ¹⁴⁹Sm. Therefore, the precise determination by ¹⁴⁹Sm Mössbauer spectroscopy is difficult. The recent development of synchrotron-radiation-based Mössbauer spectroscopy allows the isomer shifts to be determined more precisely than previously with the help of wellcollimated synchrotron radiation. In particular, the time-window effect assists the precise determination of hyperfine interactions in the ¹⁴⁹Sm Mössbauer transition because this effect enables us to measure spectra with higher energy resolution than natural linewidth determined by the lifetime of the excited states. Meanwhile, highenergy-resolution measurements to determine center shifts by SR-based Mössbauer spectroscopy enable us to observe the second-order Doppler shift, which has not been discussed, particularly for heavy Mössbauer nuclei. We have discussed the precise determination of isomer shifts and the observation of the second-order Doppler shift using ¹⁴⁹Sm synchrotron-radiation-based Mössbauer spectroscopy.     

Mott-Insulator-Superfluid Phase Transition with Coupled-Cavity Frequency Conversion System

An array of coupled cavities, each of which contains a triangle-down-level atom, is investigated. An effective Hamiltonian can be achieved under the strong classical driving. We can control the transition between Mott-insulator and superfluid states by the classical driving. The frequency conversion in one site has the same effects of nonlinear in BH hamiltonian which can induce insulator-superfluid states.