Equivalent Theories and Changing Hamiltonian Observables in General Relativity

Change and local spatial variation are missing in Hamiltonian general relativity according to the most common definition of observables as having 0 Poisson bracket with all first-class constraints. But other definitions of observables have been proposed. In pursuit of Hamiltonian–Lagrangian equivalence, Pons, Salisbury and Sundermeyer use the Anderson–Bergmann–Castellani gauge generator G, a tuned sum of first-class constraints. Kucha? waived the 0 Poisson bracket condition for the Hamiltonian constraint to achieve changing observables. A systematic combination of the two reforms might use the gauge generator but permit non-zero Lie derivative Poisson brackets for the external gauge symmetry of General Relativity. Fortunately one can test definitions of observables by calculation using two formulations of a theory, one without gauge freedom and one with gauge freedom. The formulations, being empirically equivalent, must have equivalent observables. For de Broglie-Proca non-gauge massive electromagnetism, all constraints are second-class, so everything is observable. Demanding equivalent observables from gauge Stueckelberg–Utiyama electromagnetism, one finds that the usual definition fails while the Pons–Salisbury–Sundermeyer definition with G succeeds. This definition does not readily yield change in GR, however. Should GR’s external gauge freedom of general relativity share with internal gauge symmetries the 0 Poisson bracket (invariance), or is covariance (a transformation rule) sufficient? A graviton mass breaks the gauge symmetry (general covariance), but it can be restored by parametrization with clock fields. By requiring equivalent observables, one can test whether observables should have 0 or the Lie derivative as the Poisson bracket with the gauge generator G. The latter definition is vindicated by calculation. While this conclusion has been reported previously, here the calculation is given in some detail.     

Higher-dimensional black holes with Dirac–Born–Infeld (DBI) global defects

It is well-known that the exact solution of non-linear \(\sigma \) model coupled to gravity can be perceived as an exterior gravitational field of a global monopole. Here we study Einstein’s equations coupled to a non-linear \(\sigma \) model with Dirac–Born–Infeld (DBI) kinetic term in D dimensions. The solution describes a metric around a DBI global defects. When the core is smaller than its Schwarzschild radius it can be interpreted as a black hole having DBI scalar hair with deficit conical angle. The solutions exist for all D, but they can be expressed as polynomial functions in r only when D is even. We give conditions for the mass M and the scalar charge \(\eta \) in the extremal case. We also investigate the thermodynamic properties of the black holes in canonical ensemble. The monopole alter the stability differently in each dimensions. As the charge increases the black hole radiates more, in contrast to its counterpart with ordinary global defects where the Hawking temperature is minimum for critical \(\eta \). This behavior can also be observed for variation of DBI coupling, \(\beta \). As it gets stronger (\(\beta \ll 1\)) the temperature increases. By studying the heat capacity we can infer that there is no phase transition in asymptotically-flat spacetime. The AdS black holes, on the other hand, undergo a first-ordered phase transition in the Hawking–Page type. The increase of the DBI coupling renders the phase transition happen for larger radius.     

On/off spin-crossover phenomenon and control of the transition temperature in assembled Iron(II) complexes

The present study reveals the on/off of spin-crossover (SCO) phenomenon in assembled Fe(II) complexes bridged by bis(pyridyl) type ligand. Whether SCO phenomenon occurs or not in assembled Fe(II) complexes bridged by bis(pyridyl) type ligand is determined by local structure around iron atom. SCO phenomenon occurs when the coordinating pyridines facing to each other across the iron atom are propeller type, while the phenomenon does not occur when they are parallel type or distorted propeller type. DFT calculation explained that, in the shortening of Fe-pyridine bonds when changing from high-spin state to low-spin state, the pyridines of propeller type can approach the iron atom with smaller steric hindrance than those of parallel and distorted propeller type complexes. The local structure is controlled by introducing methyl substituent and introducing π-system, changing SCO phenomenon. And the transition temperature of SCO is also controlled in assembled complexes bridged by 1,2-bis(4-pyridyl)ethane by mixing anionic ligand.     

Mathieu and Heun Solutions to the Wheeler–De Witt Equation for Hyperbolic Universes

For the spatially open Friedmann–Robertson–Walker (FRW) Universe with stiff matter and radiation as non-interacting matter sources, the scale function coming from the integration of the Friedmann equation is expressed in terms of elliptic integrals. For a negative cosmological constant, we identify the allowed ranges for the model’s parameters. Within the quantum analysis, the Wheeler–De Witt (WDW) equation turns into a modified Morse equation whose solutions are Mathieu and Heun functions.     

Center-of-Mass Tomography and Wigner Function for Multimode Photon States

Tomographic probability representation of multimode electromagnetic field states in the scheme of center-of-mass tomography is reviewed. Both connection of the field state Wigner function and observable Weyl symbols with the center-of-mass tomograms as well as connection of the Grönewold kernel with the center-of-mass tomographic kernel determining the noncommutative product of the tomograms are obtained. The dual center-of-mass tomogram of the photon states are constructed and the dual tomographic kernel is obtained. The models of other generalized center-of-mass tomographies are discussed. Example of two-mode even and odd Schrödinger cat states is presented in details.     

Quantum Corrections for Regular Black Holes with Charge and Coupling Constant

In this paper, we use semi-classical tunneling approach to calculate the quantum corrections to the Hawking temperature as well as entropy of the Kehagias-Sftesos asymptotically flat black hole solution and charged regular black hole with Fermi-Dirac distribution. For this purpose, we apply the first law of black hole thermodynamics to investigate the semi-classical entropy of both black holes having mass as well as charge or coupling constant. For both black holes, the entropy corrections contain the logarithmic term as a leading order correction term. For Kehagias-Sftesos asymptotically flat black hole, the semi-classical Hawking temperature and black hole entropy will behave asymptotically by considering the vanishing coupling constant b = 0. We have obtained the same analysis for the corrected thermodynamical quantities for this BH. For charged regular black hole with Fermi-Dirac distribution, if we neglect the charged effects in our analysis, i.e., q = 0, then these corrections approximately leads to the Schwarzschild black hole which is already given in the literature.     

Microwave-Assisted Combustion Synthesis of ZnO:Eu Nanoparticles: Effect of Fuel Types

Nanoparticles of Europium oxide doped with Zinc oxide were synthesized via microwave-assisted combustion method. Citric acid as a simultaneous fuel and chelating agent and glycine as a fuel and mixture of these fuels were sleeted. X-Ray diffraction patterns (XRD) indicated the formation of ZnO structure with a few amount of Eu₂O₃ phase. Fourier transformation infra red (FTIR) spectra reveal the increase of ZnO₄ bonds with glycine content of fuels mixture. Scanning electron microscope (SEM) images showed the conversion of nanosphere to spongy-like structure with respect to change of fuel mixtures from citric to glycine. From transmission electron microscopy (TEM) nanoparticles of a mean size 30 nm are observed Green fluorescence emission of different samples was due to activation of self activated center of ZnO structure through transition of electron from Eu³⁺ to V_zn sites.     

Fluorescence Correlation Spectroscopy with Photobleaching Correction in Slowly Diffusing Systems

Fluorescence correlation spectroscopy (FCS) is a powerful tool to quantitatively study the diffusion of fluorescently labeled molecules. It allows in principle important questions of macromolecular transport and supramolecular aggregation in living cells to be addressed. However, the crowded environment inside the cells slows diffusion and limits the reservoir of labeled molecules, causing artifacts that arise especially from photobleaching and limit the utility of FCS in these applications. We present a method to compute the time correlation function from weighted photon arrival times, which compensates computationally during the data analysis for the effect of photobleaching. We demonstrate the performance of this method using numerical simulations and experimental data from model solutions. Using this technique, we obtain correlation functions in which the effect of photobleaching has been removed and in turn recover quantitatively accurate mean-square displacements of the fluorophores, especially when deviations from an ideal Gaussian excitation volume are accounted for by using a reference calibration correlation function. This allows quantitative FCS studies of transport processes in challenging environments with substantial photobleaching like in living cells in the future.     

Fluorescent Carbon Dots as Cost-Effective and Facile Probes for Caffeic Acid Sensing via a Fluorescence Quenching Process

Caffeic acid (CA), a familiar color stabilizing reagent, has aroused general concern due to its uncontrolled addition, and thus the detection of CA is increasingly important. In our report, the bright carbon dots (CDs) were prepared via hydrothermal treatment with urea and citric acid act as raw material and their characteristics were discussed through X-ray diffraction (XRD), transmission electron microscopy (TEM) and so on. Impressively, the strong emission of the as-prepared CDs (Quantum Yield: 24.3%) decreased sharply upon a full reaction with the added CA. Hence, we first present an improved strategy for determining CA based upon the quenching of the strong emission of CDs. In this strategy, 0.79–100.0 µmol L^??1 caffeic acid could be simply detected, and a detection limit of 0.24 µmol L^??1 was allowed. Additionally, CA in red wine samples can be successfully detected by this method and the exploration of the quenching mechanism of the CA-CDs system was done.