Stationary perturbations and infinitesimal rotations of static Einstein-Yang-Mills configurations with bosonic matter

Using the Kaluza-Klein structure of stationary spacetimes, a framework for analyzing stationary perturbations of static Einstein-Yang-Mills configurations with bosonic matter fields is presented. It is shown that the perturbations giving rise to non-vanishing ADM angular momentum are governed by a self-adjoint system of equations for a set of gauge invariant scalar amplitudes. The method is illustrated for SU(2) gauge fields, coupled to a Higgs doublet or a Higgs triplet. It is argued that slowly rotating black holes arise generically in self-gravitating non-Abelian gauge theories with bosonic matter, whereas, in general, soliton solutions do not have rotating counterparts.Comment: 8 pages, revtex, no figure

A Mass Bound for Spherically Symmetric Black Hole Spacetimes

Requiring that the matter fields are subject to the dominant energy condition, we establish the lower bound $(4\pi)^{-1} \kappa {\cal A}$ for the total mass $M$ of a static, spherically symmetric black hole spacetime. (${\cal A}$ and $\kappa$ denote the area and the surface gravity of the horizon, respectively.) Together with the fact that the Komar integral provides a simple relation between $M - (4\pi)^{-1} \kappa A$ and the strong energy condition, this enables us to prove that the Schwarzschild metric represents the only static, spherically symmetric black hole solution of a selfgravitating matter model satisfying the dominant, but violating the strong energy condition for the timelike Killing field $K$ at every point, that is, $R(K,K) \leq 0$. Applying this result to scalar fields, we recover the fact that the only black hole configuration of the spherically symmetric Einstein-Higgs model with arbitrary non-negative potential is the Schwarzschild spacetime with constant Higgs field. In the presence of electromagnetic fields, we also derive a stronger bound for the total mass, involving the electromagnetic potentials and charges. Again, this estimate provides a simple tool to prove a ``no-hair'' theorem for matter fields violating the strong energy condition.Comment: 16 pages, LATEX, no figure

Dressing a black hole with non-minimally coupled scalar field hair

We investigate the possibility of dressing a four-dimensional black hole with classical scalar field hair which is non-minimally coupled to the space-time curvature. Our model includes a cosmological constant but no self-interaction potential for the scalar field. We are able to rule out black hole hair except when the cosmological constant is negative and the constant governing the coupling to the Ricci scalar curvature is positive. In this case, non-trivial hairy black hole solutions exist, at least some of which are linearly stable. However, when the coupling constant becomes too large, the black hole hair becomes unstable.Comment: 17 pages, 7 figures, uses iopart.cls. Minor changes, accepted for publication in Classical and Quantum Gravit

First clear evidence of quantum chaos in the bound states of an atomic nucleus

We study the spectral fluctuations of the $^{208}$Pb nucleus using the complete experimental spectrum of 151 states up to excitation energies of $6.20$ MeV recently identified at the Maier-Leibnitz-Laboratorium at Garching, Germany. For natural parity states the results are very close to the predictions of Random Matrix Theory (RMT) for the nearest-neighbor spacing distribution. A quantitative estimate of the agreement is given by the Brody parameter $\omega$, which takes the value $\omega=0$ for regular systems and $\omega \simeq 1$ for chaotic systems. We obtain $\omega=0.85 \pm 0.02$ which is, to our knowledge, the closest value to chaos ever observed in experimental bound states of nuclei. By contrast, the results for unnatural parity states are far from RMT behavior. We interpret these results as a consequence of the strength of the residual interaction in $^{208}$Pb, which, according to experimental data, is much stronger for natural than for unnatural parity states. In addition our results show that chaotic and non-chaotic nuclear states coexist in the same energy region of the spectrum.Comment: 9 pages, 1 figur

Pulsation of Spherically Symmetric Systems in General Relativity

The pulsation equations for spherically symmetric black hole and soliton solutions are brought into a standard form. The formulae apply to a large class of field theoretical matter models and can easily be worked out for specific examples. The close relation to the energy principle in terms of the second variation of the Schwarzschild mass is also established. The use of the general expressions is illustrated for the Einstein-Yang-Mills and the Einstein-Skyrme system.Comment: 21 pages, latex, no figure

Substituting the main group element in cobalt - iron based Heusler alloys: Co2_2FeAl1−x_{1-x}Six_x

This work reports about electronic structure calculations for the Heusler compound Co$_2$FeAl$_{1-x}$Si$_x$. Particular emphasis was put on the role of the main group element in this compound. The substitution of Al by Si leads to an increase of the number of valence electrons with increasing Si content and may be seen as electron-doping. Self-consistent electronic structure calculations were performed to investigate the consequences of the electron doping for the magnetic properties. The series Co$_2$FeAl$_{1-x}$Si$_x$ is found to exhibit half-metallic ferromagnetism and the magnetic moment follows the Slater-Pauling rule. It is shown that the electron-doping stabilises the gap in the minority states for $x=0.5$.Comment: J. Phys. D (accepted

Magnetic charge, angular momentum and negative cosmological constant

We argue that there are no axially symmetric rotating monopole solutions for a Yang-Mills-Higgs theory in flat spacetime background. We construct axially symmetric Yang-Mills-Higgs solutions in the presence of a negative cosmological constant, carrying magnetic charge $n$ and a nonvanishing electric charge. However, these solution are also nonrotating.Comment: 17 pages, LaTeX, 7 figure

Beyond the Heisenberg time: Semiclassical treatment of spectral correlations in chaotic systems with spin 1/2

The two-point correlation function of chaotic systems with spin 1/2 is evaluated using periodic orbits. The spectral form factor for all times thus becomes accessible. Equivalence with the predictions of random matrix theory for the Gaussian symplectic ensemble is demonstrated. A duality between the underlying generating functions of the orthogonal and symplectic symmetry classes is semiclassically established

Semiclassical Approach to Chaotic Quantum Transport

We describe a semiclassical method to calculate universal transport properties of chaotic cavities. While the energy-averaged conductance turns out governed by pairs of entrance-to-exit trajectories, the conductance variance, shot noise and other related quantities require trajectory quadruplets; simple diagrammatic rules allow to find the contributions of these pairs and quadruplets. Both pure symmetry classes and the crossover due to an external magnetic field are considered.Comment: 33 pages, 11 figures (appendices B-D not included in journal version

Semiclassical Theory for Parametric Correlation of Energy Levels

Parametric energy-level correlation describes the response of the energy-level statistics to an external parameter such as the magnetic field. Using semiclassical periodic-orbit theory for a chaotic system, we evaluate the parametric energy-level correlation depending on the magnetic field difference. The small-time expansion of the spectral form factor $K(\tau)$ is shown to be in agreement with the prediction of parameter dependent random-matrix theory to all orders in $\tau$.Comment: 25 pages, no figur