Covariant holographic entanglement negativity

We propose a covariant holographic conjecture for the entanglement negativity of bipartite mixed states in \((1+1)\)-dimensional conformal field theories dual to bulk non static \(AdS_{3}\) configurations. Application of our conjecture to \((1+1)\)-dimensional conformal field theories dual to bulk non extremal and extremal rotating BTZ black holes exactly reproduce the corresponding entanglement negativity obtained through the replica technique, in the large central charge limit. We briefly discuss the issue of the generalization of our conjecture to higher dimensions.     

Correlation of size and oxygen bonding at the interface of Si nanocrystal in Si–SiO2 nanocomposite: A Raman mapping study

Raman spectroscopy/mapping is used to investigate the variation of Si phonon wavenumbers, i.e., lower wavenumber (LW ~ 495–510 cm⁻¹) and higher wavenumber (HW ~ 515–519 cm⁻¹) phonons, observed in Si–SiO₂ multilayer nanocomposite (NCp) grown using pulsed laser deposition. Sensitivity of Raman spectroscopy as a local probe to surface/interface is effectively used to show that LW and HW phonons originate at surface (Si–SiO₂ interface) and core of Si nanocrystals, respectively. The consistent picture of this understanding is developed using Raman spectroscopy monitored laser heating/annealing and cooling experiment at the site of the desired wavenumber, chosen with the help of Raman mapping. Raman spectra calculations for Si₄₁ cluster with oxygen and hydrogen termination show strong mode at 512 cm⁻¹ for oxygen terminated cluster corresponding to the vibration of surface Si atoms. This supports our attribution of LW phonons to be originating at the Si–SiO₂ surface/interface. These results along with XPS show that nature of interface (oxygen bonding) in turn depends on the size of nanocrystals and LW phonons originate at the surface of smaller Si nanocrystals. The understanding developed can conclude the ongoing debate on large variation in Si phonon wavenumbers of Si–SiO₂ NCps in the literature. Copyright © 2015 John Wiley & Sons, Ltd.