Two Dimensional Quantum Dilaton Gravity and the Positivity of Energy

Using an argument due to Regge and Teitelboim, an expression for the ADM mass of 2d quantum dilaton gravity is obtained. By evaluating this expression we establish that the quantum theories which can be written as a Liouville-like theory, have a lower bound to energy, provided there is no critical boundary. This fact is then reconciled with the observation made earlier that the Hawking radiation does not appear to stop. The physical picture that emerges is that of a black hole in a bath of quantum radiation. We also evaluate the ADM mass for the models with RST boundary conditions and find that negative values are allowed. The Bondi mass of these models goes to zero for large retarded times, but becomes negative at intermediate times in a manner that is consistent with the thunderpop of RST.Comment: 16 pages, phyzzx, COLO-HEP-309. (Confusing points in previous version clarified, discussion of ADM and Bondi masses in RST case added.

Anodically polarized nickel electrodes in DMSO or DMF solutions of pseudohalide ions: IR spectroelectrochemical studies

A novel subtractively normalized interfacial Fourier transform infrared spectroscopic (SNIFTIRS) investigation of anodically polarized nickel electrodes in pseudohalide-containing DMF or DMSO solutions (i.e. OCN⁻, SCN⁻, SeCN⁻), in supporting electrolyte, tetrabutylammonium perchlorate (TBAP), is presented. In general, the data showed that nickel demonstrated irreversible anodic dissolution in all solutions studied at very high values of the applied potential, > +500 mV (AgCl/Ag). The predominant speciation of nickel in these systems was as complex ions consisting of Ni²⁺ ion complexed to pseudohalide ions and solvent molecules. Insoluble films and dissolved CO₂ were also detected, though mostly in the Ni/OCN⁻ systems studied. Ni(II)/pseudohalide complex ion species detected were modeled using solutions containing Ni²⁺ ion mixed with pseudohalide ion in different mole ratios. In general, the Ni/OCN⁻ electrochemical system behaved differently relative to those of Ni/SCN⁻ and Ni/SeCN⁻ due to the difference in colors observed in cell solutions after SNIFTIRS experiments which was mirrored in the model solutions. Ni(II)-cyanate species had a different, coordination geometry and gave a characteristic bright blue color due possibly to Ni(NCO)₄²⁻ ion while Ni(II) thiocyanate and selenocyanate complex ion species had octahedral coordination geometries containing solvent and one coordinated pseudohalide ion and formed greeny yellow solutions

A Comparison of Supersymmetry Breaking and Mediation Mechanisms

We give a unified treatment of different models of supersymmetry breaking and mediation from a four dimensional effective field theory standpoint. In particular a comparison between GMSB and various gravity mediated versions of SUSY breaking shows that, once the former is embedded within a SUGRA framework, there is no particular advantage to that mechanism from the point of view of FCNC suppression. We point out the difficulties of all these scenarios - in particular the cosmological modulus problem. We end with a discussion of possible string theory realizations.Comment: Added clarifications and references, 20 page

Dimensional reduction from entanglement in Minkowski space

Using a quantum field theoretic setting, we present evidence for dimensional reduction of any sub-volume of Minkowksi space. First, we show that correlation functions of a class of operators restricted to a sub-volume of D-dimensional Minkowski space scale as its surface area. A simple example of such area scaling is provided by the energy fluctuations of a free massless quantum field in its vacuum state. This is reminiscent of area scaling of entanglement entropy but applies to quantum expectation values in a pure state, rather than to statistical averages over a mixed state. We then show, in a specific case, that fluctuations in the bulk have a lower-dimensional representation in terms of a boundary theory at high temperature.Comment: 9 pages, changes to presentation, some content corrections, version published in JHE

The Problem of Time and Quantum Black Holes

We discuss the derivation of the so-called semi-classical equations for both mini-superspace and dilaton gravity. We find that there is no systematic derivation of a semi-classical theory in which quantum mechanics is formulated in a space-time that is a solution of Einstein's equation, with the expectation value of the matter stress tensor on the right-hand side. The issues involved are related to the well-known problems associated with the interpretation of the Wheeler-deWitt equation in quantum gravity, including the problem of time. We explore the de Broglie-Bohm interpretation of quantum mechanics (and field theory) as a way of spontaneously breaking general covariance, and thereby giving meaning to the equations that many authors have been using to analyze black hole evaporation. We comment on the implications for the ``information loss" problem.Comment: 30 pages, COLO-HEP-33

Determination of the Aspect-ratio Distribution of Gold Nanorods in a Colloidal Solution using UV-visible absorption spectroscopy

Knowledge of the distribution of the aspect ratios (ARs) in a chemically-synthesized colloidal solution of Gold Nano Rods (GNRs) is an important measure in determining the quality of synthesis, and consequently the performance of the GNRs generated for various applications. In this work, an algorithm has been developed based on the Bellman Principle of Optimality to readily determine the AR distribution of synthesized GNRs in colloidal solutions. This is achieved by theoretically fitting the longitudinal plasmon resonance of GNRs obtained by UV-visible spectroscopy. The AR distribution obtained from the use of the algorithm developed have shown good agreement with those theoretically generated one as well as with the previously reported results. After bench-marking, the algorithm has been applied to determine the mean and standard deviation of the AR distribution of two GNRs solutions synthesized and examined in this work. The comparison with experimentally derived results from the use of expensive Transmission Electron Microscopic images and Dynamic Light Scattering technique shows that the algorithm developed offers a fast and thus potentially cost-effective solution to determine the quality of the synthesized GNRs specifically needed for many potential applications for the advanced sensor systems

Hamiltonian Approach to 2D Dilaton-Gravities and Invariant Adm Mass

The formula existing in the literature for the ADM mass of 2D dilaton gravity is incomplete. For example, in the case of an infalling matter shockwave this formula fails to give a time-independent mass, unless a very special coordinate system is chosen. We carefully carry out the canonical formulation of 2D dilaton gravity theories (classical, CGHS and RST). As in 4D general relativity one must add a boundary term to the bulk Hamiltonian to obtain a well-defined variational problem. This boundary term coincides with the numerical value of the Hamiltonian and gives the correct mass which obviously is time-independent.Comment: revised, 12 pages, PUPT-1379; we added a reference and corrected some minor typo

Thermodynamics and area in Minkowski space: Heat capacity of entanglement

Tracing over the degrees of freedom inside (or outside) a sub-volume V of Minkowski space in a given quantum state |psi>, results in a statistical ensemble described by a density matrix rho. This enables one to relate quantum fluctuations in V when in the state |psi>, to statistical fluctuations in the ensemble described by rho. These fluctuations scale linearly with the surface area of V. If V is half of space, then rho is the density matrix of a canonical ensemble in Rindler space. This enables us to `derive' area scaling of thermodynamic quantities in Rindler space from area scaling of quantum fluctuations in half of Minkowski space. When considering shapes other than half of Minkowski space, even though area scaling persists, rho does not have an interpretation as a density matrix of a canonical ensemble in a curved, or geometrically non-trivial, background.Comment: 17 page

Normal Bundles, Pfaffians and Anomalies

We deal with the problem of diffeomorphism anomaly in theories with branes. In particular we thoroughly analyze the problem of the residual chiral anomaly of a five-brane immersed in M-theory, paying attention to its global formulation in the five-brane world-volume. We conclude that the anomaly can be canceled by a {\it local} counterterm in the five-brane world-volume.Comment: 17 pages, Latex, sign convention changed, typos correcte

Semiclassical Approach to Black Hole Evaporation

Black hole evaporation may lead to massive or massless remnants, or naked singularities. This paper investigates this process in the context of two quite different two dimensional black hole models. The first is the original CGHS model, the second is another two dimensional dilaton-gravity model, but with properties much closer to physics in the real, four dimensional, world. Numerical simulations are performed of the formation and subsequent evaporation of black holes and the results are found to agree qualitatively with the exactly solved modified CGHS models, namely that the semiclassical approximation breaks down just before a naked singularity appears.Comment: 15 pages, PUPT-1340, harvmac, 11 figures available on reques