Entanglement as a source of black hole entropy

We review aspects of black hole thermodynamics, and show how entanglement of a quantum field between the inside and outside of a horizon can account for the area-proportionality of black hole entropy, provided the field is in its ground state. We show that the result continues to hold for Coherent States and Squeezed States, while for Excited States, the entropy scales as a power of area less than unity. We also identify location of the degrees of freedom which give rise to the above entropy.Comment: 12 pages, latex, 5 figures. Invited talk by SD at `Recent Developments in Gravity' (NEB XII), Nafplion, Greece, 30 June 2006. To appear in Journal of Physics: Conference Series; V2: References added, Minor changes to match published versio

Where are the black hole entropy degrees of freedom ?

Understanding the area-proportionality of black hole entropy (the `Area Law') from an underlying fundamental theory has been one of the goals of all models of quantum gravity. A key question that one asks is: where are the degrees of freedom giving rise to black hole entropy located? Taking the point of view that entanglement between field degrees of freedom inside and outside the horizon can be a source of this entropy, we show that when the field is in its ground state, the degrees of freedom near the horizon contribute most to the entropy, and the area law is obeyed. However, when it is in an excited state, degrees of freedom far from the horizon contribute more significantly, and deviations from the area law are observed. In other words, we demonstrate that horizon degrees of freedom are responsible for the area law.Comment: 5 pages, 3 eps figures, uses Revtex4, References added, Minor changes to match published versio

Josephson junction array type I-V characteristics of quench-condensed ultra thin films of Bi

In this communication we report studies of d.c current-voltage (I-V) characteristics of ultra thin films of Bi, quench condensed on single crystal sapphire substrates at T = 15K. The hysteretic I-V characteristics are explained using a resistively and capacitively shunted junction (RCSJ) model of Josephson junction arrays. The Josephson coupling energy($E_J$) and the charging energy($E_c$) are calculated for different thickness($d$) values. A low resistance state is found in the low current regime below the critical current, $I_c$. This resistance $R_0$ is found to have a minimum at a particular thickness ($d_c$) value. Reflection High Energy Electron Diffraction (RHEED) studies are done on these films. A distinct appearance of a diffuse ring near $d_c$ is observed in the diffraction images, consistent with the recent STM studies(Ekinci and Valles, PRL {\bf 82}(1999) 1518). These films show an irreversible annealing when temperature is increased. The annealing temperature ($T_a$) also has a maximum at the same thickness. Althoguh the R$_s$ vs T of quench condensed Bi films suggest that the films are uniform, our results indicate that even in thick films, the order parameter is not fully developed over the complete area of the film. These results are discussed qualitatively.Comment: 6 pages, 6 figure

Quasi-Normal Modes of Schwarzschild Anti-De Sitter Black Holes: Electromagnetic and Gravitational Perturbations

We study the quasi-normal modes (QNM) of electromagnetic and gravitational perturbations of a Schwarzschild black hole in an asymptotically Anti-de Sitter (AdS) spacetime. Some of the electromagnetic modes do not oscillate, they only decay, since they have pure imaginary frequencies. The gravitational modes show peculiar features: the odd and even gravitational perturbations no longer have the same characteristic quasinormal frequencies. There is a special mode for odd perturbations whose behavior differs completely from the usual one in scalar and electromagnetic perturbation in an AdS spacetime, but has a similar behavior to the Schwarzschild black hole in an asymptotically flat spacetime: the imaginary part of the frequency goes as 1/r+, where r+ is the horizon radius. We also investigate the small black hole limit showing that the imaginary part of the frequency goes as r+^2. These results are important to the AdS/CFT conjecture since according to it the QNMs describe the approach to equilibrium in the conformal field theory.Comment: 2 figure

Melting of Hard Cubes

The melting transition of a system of hard cubes is studied numerically both in the case of freely rotating cubes and when there is a fixed orientation of the particles (parallel cubes). It is shown that freelly rotating cubes melt through a first-order transition, whereas parallel cubes have a continuous transition in which positional order is lost but bond-orientational order remains finite. This is interpreted in terms of a defect-mediated theory of meltingComment: 5 pages, 3 figures included. To appear in Phys. Rev.

On classical super-radiance in Kerr-Newman-anti-de Sitter black holes

We study in detail the modes of a classical scalar field on a Kerr-Newman-anti-de Sitter (KN-AdS) black hole. We construct sets of basis modes appropriate to the two possible boundary conditions (``reflective'' and ``transparent'') at time-like infinity, and consider whether super-radiance is possible. If we employ ``reflective'' boundary conditions, all modes are non-super-radiant. On the other hand, for ``transparent'' boundary conditions, the presence of super-radiance depends on our definition of positive frequency. For those KN-AdS black holes having a globally time-like Killing vector, the natural choice of positive frequency leads to no super-radiance. For other KN-AdS black holes, there is a choice of positive frequency which gives no super-radiance, but for other choices there will, in general, be super-radiance.Comment: 23 pages, 3 figures, v2: minor changes, references adde

QCD and strongly coupled gauge theories : challenges and perspectives

We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from astrophysics and cosmology to strongly coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many research streams which flow into and out of QCD, as well as a vision for future developments.Peer reviewe

Atomic layer deposition of ZrO2 thin films: Study of growth kinetics and dielectric behaviour

Thin films of ZrO2 have been deposited by ALD on Si(100) and SIMOX using two different metalorganic complexes of Zr as precursors. These films are characterized by X-ray diffraction, transmission and scanning electron microscopies, infrared spectroscopy, and electrical measurements. These show that amorphous ZrO2 films of high dielectric quality may be grown on Si(100) starting about 400degreesC. As the growth temperature is raised, the films become crystalline, the phase formed and the microstructure depending on precursor molecular structure. The phase of ZrO2 formed depends also on the relative duration of the precursor and oxygen pulses. XPS and IR spectroscopy show that films grown at low temperatures contain chemically unbound carbon, its extent depending on the precursor. C-V measurements show that films grown on Si(100) have low interface state density, low leakage current, a hysteresis width of only 10-250 mV and a dielectric constant of similar to16-25

Josephson junction array type I–V characteristics of quench-condensed ultra thin films of Bi

In this communication we report studies of dc current–voltage (I–V) characteristics of ultra thin films of Bi, quench condensed on single crystal sapphire substrates at T=15 K: The hysteretic I–V characteristics are explained using a resistively and capacitively shunted junction (RCSJ) model of Josephson junction arrays. The Josephson coupling energy $(E_J)$ and the charging energy $(E_c)$ are calculated for different thickness (d) values. A low resistance state is found in the low current regime below the critical current, $I_c$. This resistance $R_0$ is found to have a minimum at a particular thickness $(d_c)$ value. Reflection high energy electron diffraction (RHEED) studies are done on these films. A distinct appearance of a diffuse ring near $d_c$ is observed in the diffraction images, consistent with the recent STM studies (Ekinci and Valles, Phys. Rev. Lett., 82 (1999) 1518). These films show an irreversible annealing when temperature is increased. The annealing temperature $(T_a)$ also has a maximum at the same thickness. Although the $R_s$ vs T of quench-condensed Bi films suggest that the films are uniform, our results indicate that even in thick films, the order parameter is not fully developed over the complete area of the film. These results are discussed qualitatively

Filtration study for separation of solid particles from slurry generated in hydrometallurgical processing of ores and concentrates

Hydrometallurgical processes are now gaining importance with the depletion of high grade reserve of ores and concentrates. Such materials can not be processed econom-ically by the pyrometallurgical processes due to high energy consumption. In the hydrometallurgical processes, the low and complex ores are processed to recover metallic values in the form of salt/ metal followiing leaching, solvent extraction, precipitation, electrolysis etc. In this proces, the separation of solid from the liquid is an important unit operation for the development of the process. The slurry obtained in leaching or preci-pitation needs to be treated for the separation of the solid from the leach liquor before proceeding to metal recovery by solvent extraction, ion exchange, electrolysis etc. This can be achieved with the applicaion of various available techniques such as sedimentation, centrifuga-tion, bulk-flotation, hydro-cycloning etc. Sedimentation followed by filtration is the widely used industrially important techniques for the separation of solids from slurry. It includes cake filtration, thickening; floccu-lation and deliquoring of cakes