Making electromagnetic wavelets

Electromagnetic wavelets are constructed using scalar wavelets as superpotentials, together with an appropriate polarization. It is shown that oblate spheroidal antennas, which are ideal for their production and reception, can be made by deforming and merging two branch cuts. This determines a unique field on the interior of the spheroid which gives the boundary conditions for the surface charge-current density necessary to radiate the wavelets. These sources are computed, including the impulse response of the antenna.Comment: 29 pages, 4 figures; minor corrections and addition

A Weak Gravitational Lensing Analysis of Abell 2390

We report on the detection of dark matter in the cluster Abell 2390 using the weak gravitational distortion of background galaxies. We find that the cluster light and total mass distributions are quite similar over an angular scale of \simeq 7^\prime \;(1 \Mpc). The cluster galaxy and mass distributions are centered on the cluster cD galaxy and exhibit elliptical isocontours in the central \simeq 2^\prime \; (280 \kpc). The major axis of the ellipticity is aligned with the direction defined by the cluster cD and a ``straight arc'' located $\simeq 38^{\prime\prime}$ to the northwest. We determined the radial mass-to-light profile for this cluster and found a constant value of $(320 \pm 90) h\; M_\odot/L_{\odot V}$, which is consistent with other published determinations. We also compared our weak lensing azimuthally averaged radial mass profile with a spherical mass model proposed by the CNOC group on the basis of their detailed dynamical study of the cluster. We find good agreement between the two profiles, although there are weak indications that the CNOC density profile may be falling more steeply for $\theta\geq 3^\prime$ (420\kpc).Comment: 14 pages, latex file. Postscript file and one additional figure are available at ftp://magicbean.berkeley.edu/pub/squires/a2390/massandlight.ps.g

Global stability analysis of birhythmicity in a self-sustained oscillator

We analyze global stability properties of birhythmicity in a self-sustained system with random excitations. The model is a multi-limit cycles variation of the van der Pol oscillatorintroduced to analyze enzymatic substrate reactions in brain waves. We show that the two frequencies are strongly influenced by the nonlinear coefficients $\alpha$ and $\beta$. With a random excitation, such as a Gaussian white noise, the attractor's global stability is measured by the mean escape time $\tau$ from one limit-cycle. An effective activation energy barrier is obtained by the slope of the linear part of the variation of the escape time $\tau$ versus the inverse noise-intensity 1/D. We find that the trapping barriers of the two frequencies can be very different, thus leaving the system on the same attractor for an overwhelming time. However, we also find that the system is nearly symmetric in a narrow range of the parameters.Comment: 17 pages, 8 figures, to appear on Choas, 201

Symmetrization and enhancement of the continuous Morlet transform

The forward and inverse wavelet transform using the continuous Morlet basis may be symmetrized by using an appropriate normalization factor. The loss of response due to wavelet truncation is addressed through a renormalization of the wavelet based on power. The spectral density has physical units which may be related to the squared amplitude of the signal, as do its margins the mean wavelet power and the integrated instant power, giving a quantitative estimate of the power density with temporal resolution. Deconvolution with the wavelet response matrix reduces the spectral leakage and produces an enhanced wavelet spectrum providing maximum resolution of the harmonic content of a signal. Applications to data analysis are discussed.Comment: 12 pages, 8 figures, 2 tables, minor revision, final versio

Helicity, polarization, and Riemann-Silberstein vortices

Riemann-Silberstein (RS) vortices have been defined as surfaces in spacetime where the complex form of a free electromagnetic field given by F=E+iB is null (F.F=0), and they can indeed be interpreted as the collective history swept out by moving vortex lines of the field. Formally, the nullity condition is similar to the definition of "C-lines" associated with a monochromatic electric or magnetic field, which are curves in space where the polarization ellipses degenerate to circles. However, it was noted that RS vortices of monochromatic fields generally oscillate at optical frequencies and are therefore unobservable while electric and magnetic C-lines are steady. Here I show that under the additional assumption of having definite helicity, RS vortices are not only steady but they coincide with both sets of C-lines, electric and magnetic. The two concepts therefore become one for waves of definite frequency and helicity. Since the definition of RS vortices is relativistically invariant while that of C-lines is not, it may be useful to regard the vortices as a wideband generalization of C-lines for waves of definite helicity.Comment: 5 pages, no figures. Submitted to J of Optics A, special issue on Singular Optics; minor changes from v.

Effective Fokker-Planck Equation for Birhythmic Modified van der Pol Oscillator

We present an explicit solution based on the phase-amplitude approximation of the Fokker-Planck equation associated with the Langevin equation of the birhythmic modified van der Pol system. The solution enables us to derive probability distributions analytically as well as the activation energies associated to switching between the coexisting different attractors that characterize the birhythmic system. Comparing analytical and numerical results we find good agreement when the frequencies of both attractors are equal, while the predictions of the analytic estimates deteriorate when the two frequencies depart. Under the effect of noise the two states that characterize the birhythmic system can merge, inasmuch as the parameter plane of the birhythmic solutions is found to shrink when the noise intensity increases. The solution of the Fokker-Planck equation shows that in the birhythmic region, the two attractors are characterized by very different probabilities of finding the system in such a state. The probability becomes comparable only for a narrow range of the control parameters, thus the two limit cycles have properties in close analogy with the thermodynamic phases

Coherent light transport in a cold Strontium cloud

We study light coherent transport in the weak localization regime using magneto-optically cooled strontium atoms. The coherent backscattering cone is measured in the four polarization channels using light resonant with a J=0 to J=1 transition of the Strontium atom. We find an enhancement factor close to 2 in the helicity preserving channel, in agreement with theoretical predictions. This observation confirms the effect of internal structure as the key mechanism for the contrast reduction observed with an Rubidium cold cloud (see: Labeyrie et al., PRL 83, 5266 (1999)). Experimental results are in good agreement with Monte-Carlo simulations taking into account geometry effects.Comment: 4 pages, 2 figure

Thermoelectric power in one-dimensional Hubbard model

The thermoelectric power S is studied within the one-dimensional Hubbard model using the linear response theory and the numerical exact-diagonalization method for small systems. While both the diagonal and off-diagonal dynamical correlation functions of particle and energy current are singular within the model even at temperature T>0, S behaves regularly as a function of frequency $\omega$ and T. Dependence on the electron density n below the half-filling reveals a change of sign of S at n_0=0.73+/-0.07 due to strong correlations, in the whole T range considered. Approaching half-filling S is hole-like and can become large for U>>t although decreasing with T.Comment: 6 pages, 4 figure

Beam Effects on the Cryogenic System of LEP2

The LEP collider was operated during 1996 for the first time with superconducting cavities at the four interaction points. During operation for physics it was observed that the dissipated heat in the cavities is not only a function of the acceleration gradient, but depends also on beam characteristics such as intensity, bunch length and beam current. These beam effects had not been foreseen in the original heat budget of the LEP cryogenic system. The observations indicating the beam effect and its origin are presented. The available capacity of the refrigerators demonstrates that cryogenics might become a limiting factor for the performance of the LEP collider

Evolution of Lyman Break Galaxies Beyond Redshift Four

The formation rate of luminous galaxies seems to be roughly constant from z~2 to z~4 from the recent observations of Lyman break galaxies (LBGs) (Steidel et al 1999). The abundance of luminous quasars, on the other hand, appears to drop off by a factor of more than twenty from z~2 to z~5 (Warren, Hewett, & Osmer 1994; Schmidt, Schneider, & Gunn 1995). The difference in evolution between these two classes of objects in the overlapping, observed redshift range, z=2-4, can be explained naturally, if we assume that quasar activity is triggered by mergers of luminous LBGs and one quasar lifetime is ~10^{7-8} yrs. If this merger scenario holds at higher redshift, for the evolutions of these two classes of objects to be consistent at z>4, the formation rate of luminous LBGs is expected to drop off at least as rapidly as exp(-(z-4)^{6/5}) at z>4.Comment: in press, ApJ Letters, 15 latex pages plus 1 fi