Correction of non-linearity effects in detectors for electron spectroscopy

Using photoemission intensities and a detection system employed by many groups in the electron spectroscopy community as an example, we have quantitatively characterized and corrected detector non-linearity effects over the full dynamic range of the system. Non-linearity effects are found to be important whenever measuring relative peak intensities accurately is important, even in the low-countrate regime. This includes, for example, performing quantitative analyses for surface contaminants or sample bulk stoichiometries, where the peak intensities involved can differ by one or two orders of magnitude, and thus could occupy a significant portion of the detector dynamic range. Two successful procedures for correcting non-linearity effects are presented. The first one yields directly the detector efficiency by measuring a flat-background reference intensity as a function of incident x-ray flux, while the second one determines the detector response from a least-squares analysis of broad-scan survey spectra at different incident x-ray fluxes. Although we have used one spectrometer and detection system as an example, these methodologies should be useful for many other cases.Comment: 13 pages, 12 figure

A Note on Hartle-Hawking Vacua

The purpose of this note is to establish the basic properties--- regularity at the horizon, time independence, and thermality--- of the generalized Hartle-Hawking vacua defined in static spacetimes with bifurcate Killing horizon admitting a regular Euclidean section. These states, for free or interacting fields, are defined by a path integral on half the Euclidean section. The emphasis is on generality and the arguments are simple but formal.Comment: 5 pages, LaTe

On the Particle Definition in the presence of Black Holes

A canonical particle definition via the diagonalisation of the Hamiltonian for a quantum field theory in specific curved space-times is presented. Within the provided approach radial ingoing or outgoing Minkowski particles do not exist. An application of this formalism to the Rindler metric recovers the well-known Unruh effect. For the situation of a black hole the Hamiltonian splits up into two independent parts accounting for the interior and the exterior domain, respectively. It turns out that a reasonable particle definition may be accomplished for the outside region only. The Hamiltonian of the field inside the black hole is unbounded from above and below and hence possesses no ground state. The corresponding equation of motion displays a linear global instability. Possible consequences of this instability are discussed and its relations to the sonic analogues of black holes are addressed. PACS-numbers: 04.70.Dy, 04.62.+v, 10.10.Ef, 03.65.Db.Comment: 44 pages, LaTeX, no figures, accepted for publication in Phys. Rev.

The "physical process" version of the first law and the generalized second law for charged and rotating black holes

We investigate both the ``physical process'' version of the first law and the second law of black hole thermodynamics for charged and rotating black holes. We begin by deriving general formulas for the first order variation in ADM mass and angular momentum for linear perturbations off a stationary, electrovac background in terms of the perturbed non-electromagnetic stress-energy, $\delta T_{ab}$, and the perturbed charge current density, $\delta j^a$. Using these formulas, we prove the "physical process version" of the first law for charged, stationary black holes. We then investigate the generalized second law of thermodynamics (GSL) for charged, stationary black holes for processes in which a box containing charged matter is lowered toward the black hole and then released (at which point the box and its contents fall into the black hole and/or thermalize with the ``thermal atmosphere'' surrounding the black hole). Assuming that the thermal atmosphere admits a local, thermodynamic description with respect to observers following orbits of the horizon Killing field, and assuming that the combined black hole/thermal atmosphere system is in a state of maximum entropy at fixed mass, angular momentum, and charge, we show that the total generalized entropy cannot decrease during the lowering process or in the ``release process''. Consequently, the GSL always holds in such processes. No entropy bounds on matter are assumed to hold in any of our arguments.Comment: 35 pages; 1 eps figur

Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy

We consider a general, classical theory of gravity with arbitrary matter fields in $n$ dimensions, arising from a diffeomorphism invariant Lagrangian, \bL. We first show that \bL always can be written in a ``manifestly covariant" form. We then show that the symplectic potential current $(n-1)$-form, $\th$, and the symplectic current $(n-1)$-form, \om, for the theory always can be globally defined in a covariant manner. Associated with any infinitesimal diffeomorphism is a Noether current $(n-1)$-form, \bJ, and corresponding Noether charge $(n-2)$-form, \bQ. We derive a general ``decomposition formula" for \bQ. Using this formula for the Noether charge, we prove that the first law of black hole mechanics holds for arbitrary perturbations of a stationary black hole. (For higher derivative theories, previous arguments had established this law only for stationary perturbations.) Finally, we propose a local, geometrical prescription for the entropy, $S_{dyn}$, of a dynamical black hole. This prescription agrees with the Noether charge formula for stationary black holes and their perturbations, and is independent of all ambiguities associated with the choices of \bL, $\th$, and \bQ. However, the issue of whether this dynamical entropy in general obeys a ``second law" of black hole mechanics remains open. In an appendix, we apply some of our results to theories with a nondynamical metric and also briefly develop the theory of stress-energy pseudotensors.Comment: 30 pages, LaTe

A gravitational memory effect in "boosted" black hole perturbation theory

Black hole perturbation theory, or more generally, perturbation theory on a Schwarzschild bockground, has been applied in several contexts, but usually under the simplifying assumption that the ADM momentum vanishes, namely, that the evolution is carried out and observed in the ``center of momentum frame''. In this paper we consider some consequences of the inclusion of a non vanishing ADM momentum in the initial data. We first provide a justification for the validity of the transformation of the initial data to the ``center of momentum frame'', and then analyze the effect of this transformation on the gravitational wave amplitude. The most significant result is the possibility of a type of gravitational memory effect that appears to have no simple relation with the well known Christodoulou effect.Comment: REVTexIV, 15 pages, 2 EPS figure

The Dirichlet Casimir effect for ϕ4\phi^4 theory in (3+1) dimensions: A new renormalization approach

We calculate the next to the leading order Casimir effect for a real scalar field, within $\phi^4$ theory, confined between two parallel plates in three spatial dimensions with the Dirichlet boundary condition. In this paper we introduce a systematic perturbation expansion in which the counterterms automatically turn out to be consistent with the boundary conditions. This will inevitably lead to nontrivial position dependence for physical quantities, as a manifestation of the breaking of the translational invariance. This is in contrast to the usual usage of the counterterms in problems with nontrivial boundary conditions, which are either completely derived from the free cases or at most supplemented with the addition of counterterms only at the boundaries. Our results for the massive and massless cases are different from those reported elsewhere. Secondly, and probably less importantly, we use a supplementary renormalization procedure, which makes the usage of any analytic continuation techniques unnecessary.Comment: JHEP3 format,20 pages, 2 figures, to appear in JHE

Supersymmetric Field-Theoretic Models on a Supermanifold

We propose the extension of some structural aspects that have successfully been applied in the development of the theory of quantum fields propagating on a general spacetime manifold so as to include superfield models on a supermanifold. We only deal with the limited class of supermanifolds which admit the existence of a smooth body manifold structure. Our considerations are based on the Catenacci-Reina-Teofillatto-Bryant approach to supermanifolds. In particular, we show that the class of supermanifolds constructed by Bonora-Pasti-Tonin satisfies the criterions which guarantee that a supermanifold admits a Hausdorff body manifold. This construction is the closest to the physicist's intuitive view of superspace as a manifold with some anticommuting coordinates, where the odd sector is topologically trivial. The paper also contains a new construction of superdistributions and useful results on the wavefront set of such objects. Moreover, a generalization of the spectral condition is formulated using the notion of the wavefront set of superdistributions, which is equivalent to the requirement that all of the component fields satisfy, on the body manifold, a microlocal spectral condition proposed by Brunetti-Fredenhagen-K\"ohler.Comment: Final version to appear in J.Math.Phy

Applications of a New Proposal for Solving the "Problem of Time" to Some Simple Quantum Cosmological Models

We apply a recent proposal for defining states and observables in quantum gravity to simple models. First, we consider a Klein-Gordon particle in an ex- ternal potential in Minkowski space and compare our proposal to the theory ob- tained by deparametrizing with respect to a time slicing prior to quantiza- tion. We show explicitly that the dynamics of the deparametrization approach depends on the time slicing. Our proposal yields a dynamics independent of the choice of time slicing at intermediate times but after the potential is turned off, the dynamics does not return to the free particle dynamics. Next we apply our proposal to the closed Robertson-Walker quantum cosmology with a massless scalar field with the size of the universe as our time variable, so the only dynamical variable is the scalar field. We show that the resulting theory has the semi-classical behavior up to the classical turning point from expansion to contraction, i.e., given a classical solution which expands for much longer than the Planck time, there is a quantum state whose dynamical evolution closely approximates this classical solution during the expansion. However, when the "time" gets larger than the classical maximum, the scalar field be- comes "frozen" at its value at the maximum expansion. We also obtain similar results in the Taub model. In an Appendix we derive the form of the Wheeler- DeWitt equation for the Bianchi models by performing a proper quantum reduc- tion of the momentum constraints; this equation differs from the usual one ob- tained by solving the momentum constraints classically, prior to quantization.Comment: 30 pages, LaTeX 3 figures (postscript file or hard copy) available upon request, BUTP-94/1

Thermal partition function of photons and gravitons in a Rindler wedge

The thermal partition function of photons in any covariant gauge and gravitons in the harmonic gauge, propagating in a Rindler wedge, are computed using a local $\zeta$-function regularization approach. The correct Planckian leading order temperature dependence $T^4$ is obtained in both cases. For the photons, the existence of a surface term giving a negative contribution to the entropy is confirmed, as earlier obtained by Kabat, but this term is shown to be gauge dependent in the four-dimensional case and, therefore is discarded. It is argued that similar terms could appear dealing with any integer spin $s\geq 1$ in the massless case and in more general manifolds. Our conjecture is checked in the case of a graviton in the harmonic gauge, where different surface terms also appear, and physically consistent results arise dropping these terms. The results are discussed in relation to the quantum corrections to the black hole entropy.Comment: 29 pages, RevTeX, no figures. Minor errors corrected and a few comments changed since first submission. To be published on Phys.Rev.