Blindly detecting orbital modulations of jets from merging supermassive black holes

In the last few years before merger, supermassive black hole binaries will rapidly inspiral and precess in a magnetic field imposed by a surrounding circumbinary disk. Multiple simulations suggest this relative motion will convert some of the local energy to a Poynting-dominated outflow, with a luminosity 10^{43} erg/s * (B/10^4 G)^2(M/10^8 Msun)^2 (v/0.4 c)^2, some of which may emerge as synchrotron emission at frequencies near 1 GHz where current and planned wide-field radio surveys will operate. On top of a secular increase in power on the gravitational wave inspiral timescale, orbital motion will produce significant, detectable modulations, both on orbital periods and (if black hole spins are not aligned with the binary's total angular momenta) spin-orbit precession timescales. Because the gravitational wave merger time increases rapidly with separation, we find vast numbers of these transients are ubiquitously predicted, unless explicitly ruled out (by low efficiency $\epsilon$) or obscured (by accretion geometry f_{geo}). If the fraction of Poynting flux converted to radio emission times the fraction of lines of sight accessible $f_{geo}$ is sufficiently large (f_{geo} \epsilon > 2\times 10^{-4} for a 1 year orbital period), at least one event is accessible to future blind surveys at a nominal 10^4 {deg}^2 with 0.5 mJy sensitivity. Our procedure generalizes to other flux-limited surveys designed to investigate EM signatures associated with many modulations produced by merging SMBH binaries.Comment: Submitted to ApJ. v1 original submission; v2 minor changes in response to refere

Periodic orbit effects on conductance peak heights in a chaotic quantum dot

We study the effects of short-time classical dynamics on the distribution of Coulomb blockade peak heights in a chaotic quantum dot. The location of one or both leads relative to the short unstable orbits, as well as relative to the symmetry lines, can have large effects on the moments and on the head and tail of the conductance distribution. We study these effects analytically as a function of the stability exponent of the orbits involved, and also numerically using the stadium billiard as a model. The predicted behavior is robust, depending only on the short-time behavior of the many-body quantum system, and consequently insensitive to moderate-sized perturbations.Comment: 14 pages, including 6 figure

Scalar Casimir Energies of Tetrahedra and Prisms

New results for scalar Casimir self-energies arising from interior modes are presented for the three integrable tetrahedral cavities. Since the eigenmodes are all known, the energies can be directly evaluated by mode summation, with a point-splitting regulator, which amounts to evaluation of the cylinder kernel. The correct Weyl divergences, depending on the volume, surface area, and the edges, are obtained, which is strong evidence that the counting of modes is correct. Because there is no curvature, the finite part of the quantum energy may be unambiguously extracted. Cubic, rectangular parallelepipedal, triangular prismatic, and spherical geometries are also revisited. Dirichlet and Neumann boundary conditions are considered for all geometries. Systematic behavior of the energy in terms of geometric invariants for these different cavities is explored. Smooth interpolation between short and long prisms is further demonstrated. When scaled by the ratio of the volume to the surface area, the energies for the tetrahedra and the prisms of maximal isoareal quotient lie very close to a universal curve. The physical significance of these results is discussed.Comment: 27 pages, 11 figure

Optical Modulation in the X-Ray Binary 4U 1543-624 Revisited

The X-ray binary 4U 1543$-$624 has been provisionally identified as an ultracompact system with an orbital period of $\simeq$18~min. We have carried out time-resolved optical imaging of the binary to verify the ultra-short orbital period. Using 140\,min of high-cadence $r'$-band photometry we recover the previously-seen sinusoidal modulation and determine a period $P=18.20\pm0.09$\,min. In addition, we also see a 7.0$\times 10^{-4}$\,mag\,min$^{-1}$ linear decay, likely related to variations in the source's accretion activity. Assuming that the sinusoidal modulation arises from X-ray heating of the inner face of the companion star, we estimate a distance of 6.0--6.7\,kpc and an inclination angle of 34$^{\circ}$--61$^{\circ}$ (90\% confidence) for the binary. Given the stability of the modulation we can confirm that the modulation is orbital in origin and 4U 1543$-$624 is an ultracompact X-ray binary.Comment: 6 pages, 3 figures, accepted for publication in Publications of the Astronomical Society of Australia (PASA

Eigenstate Structure in Graphs and Disordered Lattices

We study wave function structure for quantum graphs in the chaotic and disordered regime, using measures such as the wave function intensity distribution and the inverse participation ratio. The result is much less ergodicity than expected from random matrix theory, even though the spectral statistics are in agreement with random matrix predictions. Instead, analytical calculations based on short-time semiclassical behavior correctly describe the eigenstate structure.Comment: 4 pages, including 2 figure

Transport Through Nanostructures with Asymmetric Coupling to the Leads

Using an approach to open quantum systems based on the effective non-Hermitian Hamiltonian, we fully describe transport properties for a paradigmatic model of a coherent quantum transmitter: a finite sequence of square potential barriers. We consider the general case of asymmetric external barriers and variable coupling strength to the environment. We demonstrate that transport properties are very sensitive to the degree of opening of the system and determine the parameters for maximum transmission at any given degree of asymmetry. Analyzing the complex eigenvalues of the non-Hermitian Hamiltonian, we show a double transition to a super-radiant regime where the transport properties and the structure of resonances undergo a strong change. We extend our analysis to the presence of disorder and to higher dimensions.Comment: submitted to Phys. Rev.

Refraction of a Gaussian Seaway

Refraction of a Longuet-Higgins Gaussian sea by random ocean currents creates persistent local variations in average energy and wave action. These variations take the form of lumps or streaks, and they explicitly survive dispersion over wavelength and incoming wave propagation direction. Thus, the uniform sampling assumed in the venerable Longuet-Higgins theory does not apply following refraction by random currents. Proper handling of the non-uniform sampling results in greatly increased probability of freak wave formation. The present theory represents a synthesis of Longuet-Higgins Gaussian seas and the refraction model of White and Fornberg, which considered the effect of currents on a plane wave incident seaway. Using the linearized equations for deep ocean waves, we obtain quantitative predictions for the increased probability of freak wave formation when the refractive effects are taken into account. The crest height or wave height distribution depends primarily on the ``freak index", gamma, which measures the strength of refraction relative to the angular spread of the incoming sea. Dramatic effects are obtained in the tail of this distribution even for the modest values of the freak index that are expected to occur commonly in nature. Extensive comparisons are made between the analytical description and numerical simulations.Comment: 18 pages, 10 figure