The issue of time in generally covariant theories and the Komar-Bergmann approach to observables in general relativity

Diffeomorphism-induced symmetry transformations and time evolution are distinct operations in generally covariant theories formulated in phase space. Time is not frozen. Diffeomorphism invariants are consequently not necessarily constants of the motion. Time-dependent invariants arise through the choice of an intrinsic time, or equivalently through the imposition of time-dependent gauge fixation conditions. One example of such a time-dependent gauge fixing is the Komar-Bergmann use of Weyl curvature scalars in general relativity. An analogous gauge fixing is also imposed for the relativistic free particle and the resulting complete set time-dependent invariants for this exactly solvable model are displayed. In contrast with the free particle case, we show that gauge invariants that are simultaneously constants of motion cannot exist in general relativity. They vary with intrinsic time

Effect of current corrugations on the stability of the tearing mode

The generation of zonal magnetic fields in laboratory fusion plasmas is predicted by theoretical and numerical models and was recently observed experimentally. It is shown that the modification of the current density gradient associated with such corrugations can significantly affect the stability of the tearing mode. A simple scaling law is derived that predicts the impact of small stationary current corrugations on the stability parameter $\Delta'$. The described destabilization mechanism can provide an explanation for the trigger of the Neoclassical Tearing Mode (NTM) in plasmas without significant MHD activity.Comment: Accepted to Physics of Plasma

Gossip on Weighted Networks

We investigate how suitable a weighted network is for gossip spreading. The proposed model is based on the gossip spreading model introduced by Lind et.al. on unweighted networks. Weight represents "friendship." Potential spreader prefers not to spread if the victim of gossip is a "close friend". Gossip spreading is related to the triangles and cascades of triangles. It gives more insight about the structure of a network. We analyze gossip spreading on real weighted networks of human interactions. 6 co-occurrence and 7 social pattern networks are investigated. Gossip propagation is found to be a good parameter to distinguish co-occurrence and social pattern networks. As a comparison some miscellaneous networks and computer generated networks based on ER, BA, WS models are also investigated. They are found to be quite different than the human interaction networks.Comment: 8 pages, 4 figures, 1 tabl

Lagrangian approach to a symplectic formalism for singular systems

We develop a Lagrangian approach for constructing a symplectic structure for singular systems. It gives a simple and unified framework for understanding the origin of the pathologies that appear in the Dirac-Bergmann formalism, and offers a more general approach for a symplectic formalism, even when there is no Hamiltonian in a canonical sense. We can thus overcome the usual limitations of the canonical quantization, and perform an algebraically consistent quantization for a more general set of Lagrangian systems.Comment: 30 page

A New Superwind Wolf-Rayet Galaxy Mrk 1259

We report the discovery of a starburst-driven wind (superwind) from the starburst nucleus galaxy Mrk 1259. The estimated number ratio of Wolf-Rayet (WR) to O stars amounts to ~0.09. While the nuclear emission-line region is due to usual photoionization by massive stars, the circumnuclear emission-line regions show anomalous line ratios that can be due to cooling shocks. Since the host galaxy seems to be a face-on disk galaxy and the excitation conditions of the circumnuclear emission-line regions show the spatial symmetry, we consider that we are seeing the superwind nearly from a pole-on view. Cooling shock models may explain the observed emission line ratios of the circumnuclear regions although a factor of 2 overabundance of nitrogen is necessary. All these suggest that the high-mass enhanced starburst occurred ~5X10^6 years ago in the nuclear region of Mrk 1259.Comment: To be published in the Astrophysical Journal Letters, 15 pages, 4 figure

Numerical Calculation of the Fidelity for the Kondo and the Friedel-Anderson Impurities

The fidelities of the Kondo and the Friedel-Anderson (FA) impurities are calculated numerically. The ground states of both systems are calculated with the FAIR (Friedel artificially inserted resonance) theory. The ground state in the interacting systems is compared with a nullstate in which the interaction is zero. The different multi-electron states are expressed in terms of Wilson states. The use of N Wilson states simulates the use of a large effective number N_{eff} of states. A plot of ln(F) versus N\proptoln(N_{eff}) reveals whether one has an Anderson orthogonality catastrophe at zero energy. The results are at first glance surprising. The ln(F)-ln(N_{eff}) plot for the Kondo impurity diverges for large N_{eff}. On the other hand, the corresponding plot for the symmetric FA impurity saturates for large N_{eff} when the level spacing at the Fermi level is of the order of the singlet-triplet excitation energy. The behavior of the fidelity allows one to determine the phase shift of the electron states in this regime. PACS: 75.20.Hr, 71.23.An, 71.27.+a, 05.30.-

The Nature of the Optical Light in Seyfert 2 Galaxies with Polarized Continuum

We investigate the nature of the optical continuum and stellar population in the central kpc of the Seyfert 2s Mrk 348, Mrk 573, NGC 1358 and Mrk 1210 using long-slit spectra obtained along the radio or extended emission axis. These galaxies are known to have polarized continuum-including polarized broad lines in Mrk 348 and Mrk 1210--and previous studies indicate featureless continuum (FC) contributions in the 20-50% range at 5500 A. Nevertheless, our measurements of the equivalent widths of absorption lines and continuum ratios as a function of distance from the nuclei show no dilution of the lines nor bluening of the spectrum, as expected if a blue FC was present at the nucleus in the above proportions. We investigate one possibility to account for this effect: that the stellar population at the nucleus is the same as that from the surrounding bulge and dominates the nuclear light. A spectral analysis confirms that this hypothesis works for Mrk 348, NGC 1358 and Mrk 1210, for which we find stellar contributions at the nucleus larger than 90% at all wavelengths. We find that a larger stellar population contribution to the nuclear spectra can play the role of the ``second FC'' source inferred from previous studies. Stellar population synthesis shows that the nuclear regions of Mrk 348 and Mrk 1210 have important contributions of young to intermediate age stars (0--100 Myr), not present in templates of elliptical galaxies. In the case of Mrk 1210, this is further confirmed by the detection of a ``Wolf-Rayet feature'' in the nuclear emission-line spectrum.Comment: ApJ, accepted. Uses aaspp4.sty. [22 pages