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.     

New Method of Calculating a Multiplication by using the Generalized Bernstein-Vazirani Algorithm

We present a new method of more speedily calculating a multiplication by using the generalized Bernstein-Vazirani algorithm and many parallel quantum systems. Given the set of real values \(\{a_{1},a_{2},a_{3},\ldots ,a_{N}\}\) and a function \(g:\textbf {R}\rightarrow \{0,1\}\), we shall determine the following values \(\{g(a_{1}),g(a_{2}),g(a_{3}),\ldots , g(a_{N})\}\) simultaneously. The speed of determining the values is shown to outperform the classical case by a factor of \(N\). Next, we consider it as a number in binary representation; M₁ = (g(a₁),g(a₂),g(a₃),…,g(a _N )). By using \(M\) parallel quantum systems, we have \(M\) numbers in binary representation, simultaneously. The speed of obtaining the \(M\) numbers is shown to outperform the classical case by a factor of \(M\). Finally, we calculate the product; \( M_{1}\times M_{2}\times \cdots \times M_{M}. \) The speed of obtaining the product is shown to outperform the classical case by a factor of N × M.     

Joint Remote State Preparation Schemes for Two Different Quantum States Selectively

The scheme for joint remote state preparation of two different one-qubit states according to requirement is proposed by using one four-dimensional spatial-mode-entangled KLM state as quantum channel. The scheme for joint remote state preparation of two different two-qubit states according to requirement is also proposed by using one four-dimensional spatial-mode-entangled KLM state and one three-dimensional spatial-mode-entangled GHZ state as quantum channels. Quantum non-demolition measurement, Hadamard gate operation, projective measurement and unitary transformation are included in the schemes.     

An Efficient Module for Full Adders in Quantum-dot Cellular Automata

Quantum-dot cellular automata (QCA), a new computing paradigm at nanoscale, may be a prospective alternative to conventional CMOS-based integrated circuits. Modular design methodology in QCA domain has not been widely investigated. In this paper, an efficient module with fault tolerance is proposed, which can be employed to fabricate three-input and five-input majority gates that are the fundamental primitives for designing circuits in QCA. With cells omission in the versatile module, various logic gates will be achieved, such as Nand-Nor-Inverter (NNI) gate and And-Or-Inverter (AOI) gate. Moreover, in order to seek out an efficient full adder, five various QCA full adders are designed and exhaustively compared in terms of area, complexity, latency, reliability and power dissipation and also compared with existing fault-tolerant full adders. Two simulation tools, QCADesigner and QCAPro, are utilized in the waveform simulations for verifying the correctness of proposed circuits and power consumption, respectively. The analysis results reveal that full adder V has significant improvements in contrast to its counterparts with above criteria. To test the practicability of full adder V, multi-bit adders will be designed in single-layer and compared with previous adders in terms of area, complexity and QCA cost, which proves the merits of our work.     

Detection of Single Quantum Dots in Model Systems with Sheet Illumination Microscopy

Single molecule detection and tracking provides at times the only possible method to observe the interactions of low numbers of biomolecules, inlcuding DNA, receptors and signal mediating proteins in living systems. However, most existing imaging methods do not enable both high sensitivity and non-invasive imaging of large specimens. In this study we report a new setup for selective plane illumination microscopy (SPIM), which enables fast imaging and single molecule tracking with the resolution of confocal microscopy and the optical penetration beyond 300 μm. We detect and report our instrumental figures of merit, control values of fluorescence properties of single nano crystals in comparison to both standard widefield configurations, and also values of nanocrystals in multicellular “fruiting bodies” of Dictyostelium, an excellent control as a model developmental system. In the Dictyostelium , we also report some of our first tracking of single nanocrystals with SPIM. The new SPIM setup represents a new technique, which enables fast single molecule imaging and tracking in living systems.