Bounds on length scales of classical spacetime foam models

Simple models of a classical spacetime foam are considered, which consist of identical static defects embedded in Minkowski spacetime. Plane-wave solutions of the vacuum Maxwell equations with appropriate boundary conditions at the defect surfaces are obtained in the long-wavelength limit. The corresponding dispersion relations \omega^2=\omega^2(\vec{k}) are calculated, in particular, the coefficients of the quadratic and quartic terms in \vec{k}. Astronomical observations of gamma-ray bursts and ultra-high-energy cosmic rays then place bounds on the coefficients of the dispersion relations and, thereby, on particular combinations of the fundamental length scales of the static spacetime-foam models considered. Spacetime foam models with a single length scale are excluded, even models with a length scale close to the Planck length (as long as a classical spacetime remains relevant).Comment: 22 pages with revtex4, v5: published versio

Stochastic Gravity: Theory and Applications

Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel. In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime, compute the two-point correlation functions of these perturbations and prove that Minkowski spacetime is a stable solution of semiclassical gravity. Second, we discuss structure formation from the stochastic gravity viewpoint. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a black hole and describe the metric fluctuations near the event horizon of an evaporating black holeComment: 100 pages, no figures; an update of the 2003 review in Living Reviews in Relativity gr-qc/0307032 ; it includes new sections on the Validity of Semiclassical Gravity, the Stability of Minkowski Spacetime, and the Metric Fluctuations of an Evaporating Black Hol

Quantum chemical calculations of X-ray emission spectroscopy

The calculation of X-ray emission spectroscopy with equation of motion coupled cluster theory (EOM-CCSD), time dependent density functional theory (TDDFT) and resolution of the identity single excitation configuration interaction with second order perturbation theory (RI-CIS(D)) is studied. These methods can be applied to calculate X-ray emission transitions by using a reference determinant with a core-hole, and they provide a convenient approach to compute the X-ray emission spectroscopy of large systems since all of the required states can be obtained within a single calculation removing the need to perform a separate calculation for each state. For all of the methods, basis sets with the inclusion of additional basis functions to describe core orbitals are necessary, particularly when studying transitions involving the 1s or- bitals of heavier nuclei. EOM-CCSD predicts accurate transition energies when compared with experiment, however, its application to larger systems is restricted by its computational cost and difficulty in converging the CCSD equations for a core-hole reference determinant, which become increasing problematic as the size of the system studied increases. While RI-CIS(D) gives accurate transition energies for small molecules containing first row nuclei, its application to larger systems is limited by the CIS states providing a poor zeroth order reference for perturbation theory which leads to very large errors in the computed transition energies for some states. TDDFT with standard exchange-correlation functionals predicts transition energies that are much larger than experiment. Optimization of a hybrid and short-range cor- rected functional to predict the X-ray emission transitions results in much closer agreement with EOM-CCSD. The most accurate exchange-correlation functional identified is a modified B3LYP hybrid functional with 66% Hartree-Fock exchange, denoted B66LYP, which predicts X-ray emission spectra for a range of molecules including fluorobenzene, nitrobenzene, ace- tone, dimethyl sulfoxide and CF3Cl in good agreement with experiment

Quantum Spacetime Phenomenology

I review the current status of phenomenological programs inspired by quantum-spacetime research. I stress in particular the significance of results establishing that certain data analyses provide sensitivity to effects introduced genuinely at the Planck scale. And my main focus is on phenomenological programs that managed to affect the directions taken by studies of quantum-spacetime theories.Comment: 125 pages, LaTex. This V2 is updated and more detailed than the V1, particularly for quantum-spacetime phenomenology. The main text of this V2 is about 25% more than the main text of the V1. Reference list roughly double