Hidden symmetry of the three-dimensional Einstein-Maxwell equations

It is shown how to generate three-dimensional Einstein-Maxwell fields from known ones in the presence of a hypersurface-orthogonal non-null Killing vector field. The continuous symmetry group is isomorphic to the Heisenberg group including the Harrison-type transformation. The symmetry of the Einstein-Maxwell-dilaton system is also studied and it is shown that there is the $SL(2,{\bf R})$ transformation between the Maxwell and the dilaton fields. This $SL(2,{\bf R})$ transformation is identified with the Geroch transformation of the four-dimensional vacuum Einstein equation in terms of the Ka{\l}uza-Klein mechanism.Comment: 5 page

Gauge fixing and the Hamiltonian for cylindrical spacetimes

We introduce a complete gauge fixing for cylindrical spacetimes in vacuo that, in principle, do not contain the axis of symmetry. By cylindrically symmetric we understand spacetimes that possess two commuting spacelike Killing vectors, one of them rotational and the other one translational. The result of our gauge fixing is a constraint-free model whose phase space has four field-like degrees of freedom and that depends on three constant parameters. Two of these constants determine the global angular momentum and the linear momentum in the axis direction, while the third parameter is related with the behavior of the metric around the axis. We derive the explicit expression of the metric in terms of the physical degrees of freedom, calculate the reduced equations of motion and obtain the Hamiltonian that generates the reduced dynamics. We also find upper and lower bounds for this reduced Hamiltonian that provides the energy per unit length contained in the system. In addition, we show that the reduced formalism constructed is well defined and consistent at least when the linear momentum in the axis direction vanishes. Furthermore, in that case we prove that there exists an infinite number of solutions in which all physical fields are constant both in the surroundings of the axis and at sufficiently large distances from it. If the global angular momentum is different from zero, the isometry group of these solutions is generally not orthogonally transitive. Such solutions generalize the metric of a spinning cosmic string in the region where no closed timelike curves are present.Comment: 12 pages, accepted for publication in Physical Review

Sublocalization, superlocalization, and violation of standard single parameter scaling in the Anderson model

We discuss the localization behavior of localized electronic wave functions in the one- and two-dimensional tight-binding Anderson model with diagonal disorder. We find that the distributions of the local wave function amplitudes at fixed distances from the localization center are well approximated by log-normal fits which become exact at large distances. These fits are consistent with the standard single parameter scaling theory for the Anderson model in 1d, but they suggest that a second parameter is required to describe the scaling behavior of the amplitude fluctuations in 2d. From the log-normal distributions we calculate analytically the decay of the mean wave functions. For short distances from the localization center we find stretched exponential localization ("sublocalization") in both, 1d and 2d. In 1d, for large distances, the mean wave functions depend on the number of configurations N used in the averaging procedure and decay faster that exponentially ("superlocalization") converging to simple exponential behavior only in the asymptotic limit. In 2d, in contrast, the localization length increases logarithmically with the distance from the localization center and sublocalization occurs also in the second regime. The N-dependence of the mean wave functions is weak. The analytical result agrees remarkably well with the numerical calculations.Comment: 12 pages with 9 figures and 1 tabl

Exact Hypersurface-Homogeneous Solutions in Cosmology and Astrophysics

A framework is introduced which explains the existence and similarities of most exact solutions of the Einstein equations with a wide range of sources for the class of hypersurface-homogeneous spacetimes which admit a Hamiltonian formulation. This class includes the spatially homogeneous cosmological models and the astrophysically interesting static spherically symmetric models as well as the stationary cylindrically symmetric models. The framework involves methods for finding and exploiting hidden symmetries and invariant submanifolds of the Hamiltonian formulation of the field equations. It unifies, simplifies and extends most known work on hypersurface-homogeneous exact solutions. It is shown that the same framework is also relevant to gravitational theories with a similar structure, like Brans-Dicke or higher-dimensional theories.Comment: 41 pages, REVTEX/LaTeX 2.09 file (don't use LaTeX2e !!!) Accepted for publication in Phys. Rev.

The Similarity Hypothesis in General Relativity

Self-similar models are important in general relativity and other fundamental theories. In this paper we shall discuss the ``similarity hypothesis'', which asserts that under a variety of physical circumstances solutions of these theories will naturally evolve to a self-similar form. We will find there is good evidence for this in the context of both spatially homogenous and inhomogeneous cosmological models, although in some cases the self-similar model is only an intermediate attractor. There are also a wide variety of situations, including critical pheneomena, in which spherically symmetric models tend towards self-similarity. However, this does not happen in all cases and it is it is important to understand the prerequisites for the conjecture.Comment: to be submitted to Gen. Rel. Gra

Azimuthal anisotropy and correlations in p+p, d+Au and Au+Au collisions at 200 GeV

We present the first measurement of directed flow ($v_1$) at RHIC. $v_1$ is found to be consistent with zero at pseudorapidities $\eta$ from -1.2 to 1.2, then rises to the level of a couple of percent over the range $2.4 < |\eta| < 4$. The latter observation is similar to data from NA49 if the SPS rapidities are shifted by the difference in beam rapidity between RHIC and SPS. Back-to-back jets emitted out-of-plane are found to be suppressed more if compared to those emitted in-plane, which is consistent with {\it jet quenching}. Using the scalar product method, we systematically compared azimuthal correlations from p+p, d+Au and Au+Au collisions. Flow and non-flow from these three different collision systems are discussed.Comment: Quark Matter 2004 proceeding, 4 pages, 3 figure

Azimuthal anisotropy: the higher harmonics

We report the first observations of the fourth harmonic (v_4) in the azimuthal distribution of particles at RHIC. The measurement was done taking advantage of the large elliptic flow generated at RHIC. The integrated v_4 is about a factor of 10 smaller than v_2. For the sixth (v_6) and eighth (v_8) harmonics upper limits on the magnitudes are reported.Comment: 4 pages, 6 figures, contribution to the Quark Matter 2004 proceeding

Plasma Wakefield Acceleration with a Modulated Proton Bunch

The plasma wakefield amplitudes which could be achieved via the modulation of a long proton bunch are investigated. We find that in the limit of long bunches compared to the plasma wavelength, the strength of the accelerating fields is directly proportional to the number of particles in the drive bunch and inversely proportional to the square of the transverse bunch size. The scaling laws were tested and verified in detailed simulations using parameters of existing proton accelerators, and large electric fields were achieved, reaching 1 GV/m for LHC bunches. Energy gains for test electrons beyond 6 TeV were found in this case.Comment: 9 pages, 7 figure

The energy dependence of ptp_t angular correlations inferred from mean-ptp_{t} fluctuation scale dependence in heavy ion collisions at the SPS and RHIC

We present the first study of the energy dependence of $p_t$ angular correlations inferred from event-wise mean transverse momentum fluctuations in heavy ion collisions. We compare our large-acceptance measurements at CM energies $\sqrt{s_{NN}} =$ 19.6, 62.4, 130 and 200 GeV to SPS measurements at 12.3 and 17.3 GeV. $p_t$ angular correlation structure suggests that the principal source of $p_t$ correlations and fluctuations is minijets (minimum-bias parton fragments). We observe a dramatic increase in correlations and fluctuations from SPS to RHIC energies, increasing linearly with $\ln \sqrt{s_{NN}}$ from the onset of observable jet-related fluctuations near 10 GeV.Comment: 10 pages, 4 figure

All-optical switching and strong coupling using tunable whispering-gallery-mode microresonators

We review our recent work on tunable, ultrahigh quality factor whispering-gallery-mode bottle microresonators and highlight their applications in nonlinear optics and in quantum optics experiments. Our resonators combine ultra-high quality factors of up to Q = 3.6 \times 10^8, a small mode volume, and near-lossless fiber coupling, with a simple and customizable mode structure enabling full tunability. We study, theoretically and experimentally, nonlinear all-optical switching via the Kerr effect when the resonator is operated in an add-drop configuration. This allows us to optically route a single-wavelength cw optical signal between two fiber ports with high efficiency. Finally, we report on progress towards strong coupling of single rubidium atoms to an ultra-high Q mode of an actively stabilized bottle microresonator.Comment: 20 pages, 24 figures. Accepted for publication in Applied Physics B. Changes according to referee suggestions: minor corrections to some figures and captions, clarification of some points in the text, added references, added new paragraph with results on atom-resonator interactio