On the Passage from the Quantum theory to the Semi-Classical theory

In this paper an attempt is made to understand the passage from the exact quantum treatment of the CGHS theory to the semi-classical physics discussed by many authors. We find first that to the order of accuracy to which Hawking effects are calculated in the theory, it is inconsistent to ignore correlations in the dilaton gravity sector. Next the standard Dirac or BRST procedure for implementing the constraints is followed. This leads to a set of physical states, in which however the semi-classical physics of the theory seems to be completely obscured. As an alternative, we construct a coherent state formalism, which is the natural framework for understanding the semi-classical calculations, and argue that it satisfies all necessary requirements of the theory, provided that there exist classical ghost configurations which solve an infinite set of equations. If this is the case it may be interpreted as a spontaneous breakdown of general covariance.Comment: 19 pages, COLO-HEP-31

Black Hole Physics from Liouville Theory

In a previous paper it was shown that the quantum consistency conditions for the dilaton-gravity theory of Callan et al., imply that the cosmological constant term undergoes a dilaton dependent renormalization, in such a manner that the theory can be written as a Liouville-like theory. In this paper we discuss the physical interpretation of the solutions of this theory. In particular we demonstrate explicitly how quantum corrections tame the black hole singularity. Also under the assumption that in asymptotically Minkowski coordinates, there are no incoming or outgoing ghosts, we show that the Hawking radiation rate is independent of the number of matter fields and is determined by the ghost conformal anomaly.Comment: 15 pages, phyzzx (Note on Bondi mass added to end of paper

Consequence of Hawking radiation from 2d dilaton black holes

We investigate the CGHS model through numerical calculation. The behavior of the mass function, which we introduced in our previous work as a ``local mass'', is examined. We found that the mass function takes negative values, which means that the amount of Hawking radiation becomes greater than the initial mass of the black hole as in the case of the RST model.Comment: 17pages, 5 figures (three of them are attached, the other 2 figures are available on request. Some mistakes including typographic errors have been correcte

Computational investigations of dispersion interactions between small molecules and graphene-like flakes

We investigate dispersion interactions in a selection of atomic, molecular, and molecule–surface systems, comparing high-level correlated methods with empirically corrected density functional theory (DFT). We assess the efficacy of functionals commonly used for surface-based calculations, with and without the D3 correction of Grimme. We find that the inclusion of the correction is essential to get meaningful results, but there is otherwise little to distinguish between the functionals. We also present coupled-cluster quality interaction curves for H2, NO2, H2O, and Ar interacting with large carbon flakes, acting as models for graphene surfaces, using novel absolutely localized molecular orbital based methods. These calculations demonstrate that the problems with empirically corrected DFT when investigating dispersion appear to compound as the system size increases, with important implications for future computational studies of molecule–surface interactions

Efficient enumeration of bosonic configurations with applications to the calculation of non-radiative rates

This work presents algorithms for the efficient enumeration of configuration spaces following Boltzmann-like statistics, with example applications to the calculation of non-radiative rates, and an open-source implementation. Configuration spaces are found in several areas of physics, particularly wherever there are energy levels that possess variable occupations. In bosonic systems, where there are no upper limits on the occupation of each level, enumeration of all possible configurations is an exceptionally hard problem. We look at the case where the levels need to be filled to satisfy an energy criterion, for example, a target excitation energy, which is a type of knapsack problem as found in combinatorics. We present analyses of the density of configuration spaces in arbitrary dimensions and how particular forms of kernel can be used to envelope the important regions. In this way, we arrive at three new algorithms for enumeration of such spaces that are several orders of magnitude more efficient than the naive brute force approach. Finally, we show how these can be applied to the particular case of internal conversion rates in a selection of molecules and discuss how a stochastic approach can, in principle, reduce the computational complexity to polynomial time

(Twisted) Toroidal Compactification of pp-Waves

The maximally supersymmetric type IIB pp-wave is compactified on spatial circles, with and without an auxiliary rotational twist. All spatial circles of constant radius are identified. Without the twist, an S$^1$ compactification can preserve 24, 20 or 16 supercharges. $T^2$ compactifications can preserve 20, 18 or 16 supercharges; $T^3$ compactifications can preserve 18 or 16 supercharges and higher compactifications preserve 16 supercharges. The worldsheet theory of this background is discussed. The T-dual and decompactified type IIA and M-theoretic solutions which preserve 24 supercharges are given. Some comments are made regarding the AdS parent and the CFT description.Comment: 22 pages REVTeX 4 and AMSLaTeX. v3: References and a paragraph on nine dimensional Killing spinors were added. v4: A few typos corrected and a footnote was modifie

Trace anomaly induced effective action and 2d black holes for dilaton coupled supersymmetric theories

The action for 2d dilatonic supergravity with dilaton coupled matter and dilaton multiplets is constructed. Trace anomaly and anomaly induced effective action (in components as well as in supersymmetric form) for matter supermultiplet on bosonic background are found. The one-loop effective action and large-$N$ effective action for quantum dilatonic supergravity are also calculated. Using induced effective action one can estimate the back-reaction of dilaton coupled matter to the classical black hole solutions of dilatonic supergravity. That is done on the example of supersymmetric CGHS model with dilaton coupled quantum matter where Hawking radiation which turns out to be zero is calculated. Similar 2d analysis maybe used to study spherically symmetric collapse for other models of 4d supergravity.Comment: 21 pages, LaTeX, NDA-FP-3

Modeling radiative and non-radiative pathways at both the Franck–Condon and Herzberg–Teller approximation level

Here, we present a concise model that can predict the photoluminescent properties of a given compound from first principles, both within and beyond the Franck–Condon approximation. The formalism required to compute fluorescence, Internal Conversion (IC), and Inter-System Crossing (ISC) is discussed. The IC mechanism, in particular, is a difficult pathway to compute due to difficulties associated with the computation of required bosonic configurations and non-adiabatic coupling elements. Here, we offer a discussion and breakdown on how to model these pathways at the Density Functional Theory (DFT) level with respect to its computational implementation, strengths, and current limitations. The model is then used to compute the photoluminescent quantum yield (PLQY) of a number of small but important compounds: anthracene, tetracene, pentacene, diketo-pyrrolo-pyrrole (DPP), and Perylene Diimide (PDI) within a polarizable continuum model. Rate constants for fluorescence, IC, and ISC compare well for the most part with respect to experiment, despite triplet energies being overestimated to a degree. The resulting PLQYs are promising with respect to the level of theory being DFT. While we obtained a positive result for PDI within the Franck–Condon limit, the other systems require a second order correction. Recomputing quantum yields with Herzberg–Teller terms yields PLQYs of 0.19, 0.08, 0.04, 0.70, and 0.99 for anthracene, tetracene, pentacene, DPP, and PDI, respectively. Based on these results, we are confident that the presented methodology is sound with respect to the level of quantum chemistry and presents an important stepping stone in the search for a tool to predict the properties of larger coupled systems

Hubbard physics in the PAW GW approximation

It is demonstrated that the signatures of the Hubbard Model in the strongly interacting regime can be simulated by modifying the screening in the limit of zero wavevector in Projector-Augmented Wave GW calculations for systems without significant nesting. This modification, when applied to the Mott insulator CuO, results in the opening of the Mott gap by the splitting of states at the Fermi level into upper and lower Hubbard bands, and exhibits a giant transfer of spectral weight upon electron doping. The method is also employed to clearly illustrate that the M1 and M2 forms of vanadium dioxide are fundamentally different types of insulator. Standard GW calculations are sufficient to open a gap in M1 VO2, which arise from the Peierls pairing filling the valence band, creating homopolar bonds. The valence band wavefunctions are stabilized with respect to the conduction band, reducing polarizability and pushing the conduction band eigenvalues to higher energy. The M2 structure, however, opens a gap from strong on-site interactions; it is a Mott insulator

Two-dimensional Quantum-Corrected Eternal Black Hole

The one-loop quantum corrections to geometry and thermodynamics of black hole are studied for the two-dimensional RST model. We chose boundary conditions corresponding to the eternal black hole being in the thermal equilibrium with the Hawking radiation. The equations of motion are exactly integrated. The one of the solutions obtained is the constant curvature space-time with dilaton being a constant function. Such a solution is absent in the classical theory. On the other hand, we derive the quantum-corrected metric (\ref{solution}) written in the Schwarzschild like form which is a deformation of the classical black hole solution \cite{5d}. The space-time singularity occurs to be milder than in classics and the solution admits two asymptotically flat black hole space-times lying at "different sides" of the singularity. The thermodynamics of the classical black hole and its quantum counterpart is formulated. The thermodynamical quantities (energy, temperature, entropy) are calculated and occur to be the same for both the classical and quantum-corrected black holes. So, no quantum corrections to thermodynamics are observed. The possible relevance of the results obtained to the four-dimensional case is discussed.Comment: Latex, 28 pges; minor corrections in text and abstract made and new references adde