The Effect of Sources on the Inner Horizon of Black Holes

Single pulse of null dust and colliding null dusts both transform a regular horizon into a space-like singularity in the space of colliding waves. The local isometry between such space-times and black holes extrapolates these results to the realm of black holes. However, inclusion of particular scalar fields instead of null dusts creates null singularities rather than space-like ones on the inner horizons of black holes.Comment: Final version to appear in PR

(2n×1) Reconstructions of TiO2(011) Revealed by Noncontact Atomic Force Microscopy and Scanning Tunneling Microscopy

We have used noncontact atomic force microscopy (NC-AFM) and scanning tunneling microscopy (STM) to study the rutile TiO2(011) surface. A series of (2n×1) reconstructions were observed, including two types of (4×1) reconstruction. High resolution NC-AFM and STM images indicate that the (4×1)-α phase has the same structural elements as the more widely reported (2×1) reconstruction. An array of analogous higher order (2n×1) reconstructions were also observed where n = 3-5. On the other hand, the (4×1)-β reconstruction seems to be a unique structure without higher order analogues. A model is proposed for this structure that is also based on the (2×1) reconstruction but with additional microfacets of {111} character

Fundamental Limits on the Speed of Evolution of Quantum States

This paper reports on some new inequalities of Margolus-Levitin-Mandelstam-Tamm-type involving the speed of quantum evolution between two orthogonal pure states. The clear determinant of the qualitative behavior of this time scale is the statistics of the energy spectrum. An often-overlooked correspondence between the real-time behavior of a quantum system and the statistical mechanics of a transformed (imaginary-time) thermodynamic system appears promising as a source of qualitative insights into the quantum dynamics.Comment: 6 pages, 1 eps figur

The averaged null energy condition and difference inequalities in quantum field theory

Recently, Larry Ford and Tom Roman have discovered that in a flat cylindrical space, although the stress-energy tensor itself fails to satisfy the averaged null energy condition (ANEC) along the (non-achronal) null geodesics, when the ``Casimir-vacuum" contribution is subtracted from the stress-energy the resulting tensor does satisfy the ANEC inequality. Ford and Roman name this class of constraints on the quantum stress-energy tensor ``difference inequalities." Here I give a proof of the difference inequality for a minimally coupled massless scalar field in an arbitrary two-dimensional spacetime, using the same techniques as those we relied on to prove ANEC in an earlier paper with Robert Wald. I begin with an overview of averaged energy conditions in quantum field theory.Comment: 20 page

Online Adaptive Methods, Universality and Acceleration

We present a novel method for convex unconstrained optimization that, without any modifications, ensures: (i) accelerated convergence rate for smooth objectives, (ii) standard convergence rate in the general (non-smooth) setting, and (iii) standard convergence rate in the stochastic optimization setting. To the best of our knowledge, this is the first method that simultaneously applies to all of the above settings. At the heart of our method is an adaptive learning rate rule that employs importance weights, in the spirit of adaptive online learning algorithms, combined with an update that linearly couples two sequences. An empirical examination of our method demonstrates its applicability to the above mentioned scenarios and corroborates our theoretical findings

Homodyne solid-state biased coherent detection of ultra-broadband terahertz pulses with static electric fields

We present an innovative implementation of the solid-state-biased coherent detection (SSBCD) technique, which we have recently introduced for the reconstruction of both amplitude and phase of ultra-broadband terahertz pulses. In our previous works, the SSBCD method has been operated via a heterodyne scheme, which involves demanding square-wave voltage amplifiers, phase-locked to the THz pulse train, as well as an electronic circuit for the demodulation of the readout signal. Here, we demonstrate that the SSBCD technique can be operated via a very simple homodyne scheme, exploiting plain static bias voltages. We show that the homodyne SSBCD signal turns into a bipolar transient when the static field overcomes the THz field strength, without the requirement of an additional demodulating circuit. Moreover, we introduce a differential configuration, which extends the applicability of the homodyne scheme to higher THz field strengths, also leading a two-fold improvement of the dynamic range compared to the heterodyne counterpart. Finally, we demonstrate that, by reversing the sign of the static voltage, it is possible to directly retrieve the absolute THz pulse polarity. The homodyne configuration makes the SSBCD technique of much easier access, leading to a vast range of field-resolved applications

Imaging the TiO(011)-(2 × 1) Surface using Noncontact Atomic Force Microscopy and Scanning Tunneling Microscopy

We have used noncontact atomic force microscopy (NC-AFM) and scanning tunneling microscopy (STM) to study the rutile TiO2(011)-(2 × 1) surface. NC-AFM images were obtained with several different contrasts. In particular, a zigzag contrast similar to that found in STM was observed. Simultaneously recorded NC-AFM and STM images indicate that the zigzags in NC-AFM and STM are in phase and may therefore have a similar origin. Hydrogen adatoms were also identified in NC-AFM images by comparison with STM. Sequential NC-AFM scans of the same area show that these hydrogen atoms readily diffuse between adjacent topmost oxygen atoms and follow a zigzag path, thus indicating that the H adatoms adsorb on either side of the (2 × 1) rows

The late-time singularity inside non-spherical black holes

It was long believed that the singularity inside a realistic, rotating black hole must be spacelike. However, studies of the internal geometry of black holes indicate a more complicated structure is typical. While it seems likely that an observer falling into a black hole with the collapsing star encounters a crushing spacelike singularity, an observer falling in at late times generally reaches a null singularity which is vastly different in character to the standard Belinsky, Khalatnikov and Lifschitz (BKL) spacelike singularity. In the spirit of the classic work of BKL we present an asymptotic analysis of the null singularity inside a realistic black hole. Motivated by current understanding of spherical models, we argue that the Einstein equations reduce to a simple form in the neighborhood of the null singularity. The main results arising from this approach are demonstrated using an almost plane symmetric model. The analysis shows that the null singularity results from the blueshift of the late-time gravitational wave tail; the amplitude of these gravitational waves is taken to decay as an inverse power of advanced time as suggested by perturbation theory. The divergence of the Weyl curvature at the null singularity is dominated by the propagating modes of the gravitational field. The null singularity is weak in the sense that tidal distortion remains bounded along timelike geodesics crossing the Cauchy horizon. These results are in agreement with previous analyses of black hole interiors. We briefly discuss some outstanding problems which must be resolved before the picture of the generic black hole interior is complete.Comment: 16 pages, RevTeX, 3 figures included using psfi

Quantum Inequalities for the Electromagnetic Field

A quantum inequality for the quantized electromagnetic field is developed for observers in static curved spacetimes. The quantum inequality derived is a generalized expression given by a mode function expansion of the four-vector potential, and the sampling function used to weight the energy integrals is left arbitrary up to the constraints that it be a positive, continuous function of unit area and that it decays at infinity. Examples of the quantum inequality are developed for Minkowski spacetime, Rindler spacetime and the Einstein closed universe.Comment: 19 pages, 1 table and 1 figure. RevTex styl