Stochastic model of optical variability of BL Lacertae

We use optical photometric and polarimetric data of BL Lacertae that cover a period of 22 years to study the variability of the source. The long-term observations are employed for establishing parameters of a stochastic model consisting of the radiation from a steady polarized source and a number of variable components with different polarization parameters, proposed by Hagen-Thorn et al. earlier. We infer parameters of the model from the observations using numerical simulations based on a Monte Carlo method, with values of each model parameter selected from a Gaussian distribution. We determine the best set of model parameters by comparing model distributions to the observational ones using the chi-square criterion. We show that the observed photometric and polarimetric variability can be explained within a model with a steady source of high polarization, ~40%, and with direction of polarization parallel to the parsec scale jet, along with 10+-5 sources of variable polarization.Comment: 4 pages, 10 figures, published by Astronomy and Astrophysics; v2: typos correcte

The quantitative measure and statistical distribution of fame

Fame and celebrity play an ever-increasing role in our culture. However, despite the cultural and economic importance of fame and its gradations, there exists no consensus method for quantifying the fame of an individual, or of comparing that of two individuals. We argue that, even if fame is difficult to measure with precision, one may develop useful metrics for fame that correlate well with intuition and that remain reasonably stable over time. Using datasets of recently deceased individuals who were highly renowned, we have evaluated several internet-based methods for quantifying fame. We find that some widely-used internet-derived metrics, such as search engine results, correlate poorly with human subject judgments of fame. However other metrics exist that agree well with human judgments and appear to offer workable, easily accessible measures of fame. Using such a metric we perform a preliminary investigation of the statistical distribution of fame, which has some of the power law character seen in other natural and social phenomena such as landslides and market crashes. In order to demonstrate how such findings can generate quantitative insight into celebrity culture, we assess some folk ideas regarding the frequency distribution and apparent clustering of celebrity deaths.Comment: 17 pages, 6 figure

Perturbative Expansion in the Galilean Invariant Spin One-Half Chern-Simons Field Theory

A Galilean Chern-Simons field theory is formulated for the case of two interacting spin-1/2 fields of distinct masses M and M'. A method for the construction of states containing N particles of mass M and N' particles of mass M' is given which is subsequently used to display equivalence to the spin-1/2 Aharonov-Bohm effect in the N = N' =1 sector of the model. The latter is then studied in perturbation theory to determine whether there are divergences in the fourth order (one loop) diagram. It is found that the contribution of that order is finite (and vanishing) for the case of parallel spin projections while the antiparallel case displays divergences which are known to characterize the spin zero case in field theory as well as in quantum mechanics.Comment: 14 pages LaTeX, including 2 figures using eps

The effect of time-dependent coupling on non-equilibrium steady states

Consider (for simplicity) two one-dimensional semi-infinite leads coupled to a quantum well via time dependent point interactions. In the remote past the system is decoupled, and each of its components is at thermal equilibrium. In the remote future the system is fully coupled. We define and compute the non equilibrium steady state (NESS) generated by this evolution. We show that when restricted to the subspace of absolute continuity of the fully coupled system, the state does not depend at all on the switching. Moreover, we show that the stationary charge current has the same invariant property, and derive the Landau-Lifschitz and Landauer-Buttiker formulas.Comment: 30 pages, submitte

Fluctuations of the intergalactic ionization field at redshift z ~ 2

(Abridged) Aims. To probe the spectral energy distribution (SED) of the ionizing background radiation at z ~ 2 and to specify the sources contributing to the intergalactic radiation field. Methods. The spectrum of a bright quasar HS1103+6416 (zem = 2.19) contains five successive metal-line absorption systems at zabs = 1.1923, 1.7193, 1.8873, 1.8916, and 1.9410. The systems are optically thin and reveal multiple lines of different metal ions with the ionization potentials lying in the extreme ultraviolet (EUV) range (1 Ryd to 0.2 keV). For each system, the EUV SED of the underlying ionization field is reconstructed by means of a special technique developed for solving the inverse problem in spectroscopy. For the zabs = 1.8916 system, the analysis also involves the HeI resonance lines of the Lyman series and the HeI 504 A continuum, which are seen for the first time in any cosmic object except the Sun. Results. From one system to another, the SED of the ionizing continuum changes significantly, indicating that the intergalactic ionization field at z ~ 2 fluctuates at the scale of at least Delta_z ~ 0.004. This is consistent with Delta_z ~ 0.01 estimated from HeII and HI Lyman-alpha forest measurements between the redshifts 2 and 3.Comment: 29 pages, 18 figures, 3 tables, accepted for publication in A\&