Expectations for extreme-mass-ratio bursts from the Galactic Centre

When a compact object on a highly eccentric orbit about a much more massive body passes through periapsis it emits a short gravitational wave signal known as an extreme-mass-ratio burst (EMRB). We consider stellar mass objects orbiting the massive black hole (MBH) found in the Galactic Centre. EMRBs provide a novel means of extracting information about the MBH; an EMRB from the Galactic MBH could be highly informative regarding the MBH's mass and spin if the orbital periapsis is small enough. However, to be a useful astronomical tool EMRBs must be both informative and sufficiently common to be detectable with a space-based interferometer. We construct a simple model to predict the event rate for Galactic EMRBs. We estimate there could be on average ~2 bursts in a two year mission lifetime for LISA. Stellar mass black holes dominate the event rate. Creating a sample of 100 mission realisations, we calculate what we could learn about the MBH. On average, we expect to be able to determine the MBH mass to ~1% and the spin to ~0.1 using EMRBs.Comment: 22 pages, 5 figures, 2 appendices. Minor changes to reflect published versio

High-Order Adiabatic Approximation for Non-Hermitian Quantum System and Complexization of Berry's Phase

In this paper the evolution of a quantum system drived by a non-Hermitian Hamiltonian depending on slowly-changing parameters is studied by building an universal high-order adiabatic approximation(HOAA) method with Berry's phase ,which is valid for either the Hermitian or the non-Hermitian cases. This method can be regarded as a non-trivial generalization of the HOAA method for closed quantum system presented by this author before. In a general situation, the probabilities of adiabatic decay and non-adiabatic transitions are explicitly obtained for the evolution of the non-Hermitian quantum system. It is also shown that the non-Hermitian analog of the Berry's phase factor for the non-Hermitian case just enjoys the holonomy structure of the dual linear bundle over the parameter manifold. The non-Hermitian evolution of the generalized forced harmonic oscillator is discussed as an illustrative examples.Comment: ITP.SB-93-22,17 page

Neutrino Scattering in Heterogeneous Supernova Plasmas

Neutrinos in core collapse supernovae are likely trapped by neutrino-nucleus elastic scattering. Using molecular dynamics simulations, we calculate neutrino mean free paths and ion-ion correlation functions for heterogeneous plasmas. Mean free paths are systematically shorter in plasmas containing a mixture of ions compared to a plasma composed of a single ion species. This is because neutrinos can scatter from concentration fluctuations. The dynamical response function of a heterogeneous plasma is found to have an extra peak at low energies describing the diffusion of concentration fluctuations. Our exact molecular dynamics results for the static structure factor reduce to the Debye Huckel approximation, but only in the limit of very low momentum transfers.Comment: 11 pages, 13 figure

Extreme-mass-ratio-bursts from extragalactic sources

Extreme-mass-ratio bursts (EMRBs) are a class of potentially interesting gravitational wave signals. They are produced when a compact object passes through periapsis on a highly eccentric orbit about a much more massive object; we consider stellar mass objects orbiting the massive black holes (MBHs) found in galactic centres. Such a system may emit many EMRBs before eventually completing the inspiral. There are several nearby galaxies that could yield detectable bursts. For a space-borne interferometer like the Laser Interferometer Space Antenna, sensitivity is greatest for EMRBs from MBHs of ∼106–107 M⊙, which could be detected out to ∼100 Mpc. Considering the examples of M32, NGC 4945 and NGC 4395 we investigate if extragalactic EMRB signals can provide information about their sources. This is possible, but only if the periapse radius of the orbit is small, of the order of rp ≲ 8rg, where rg = GM c− 2 is the gravitational radius of the MBH. This limits the utility of EMRBs as an astronomical tool. However, if we are lucky, we could place constraints on the mass and spin of nearby MBHs with 1 per cent precision

Thermodynamics of Finite Quantum Systems: Application to Spin Magnetism II

We extend our study of thermodynamics of a Kubo particle to temperatures smaller than the interlevel spacing. We obtain the distribution functions of spin susceptibility and heat capacity for Poisson and Wigner-Dyson level statistics. We evaluate the line shape of the Knight shift due to spin effects both in a single particle and for the ensemble average and compare it with orbital and spin-orbit contributions.Comment: 20 pages (16 text, 4 figures) uu-encoded, z-compressed PostScript. Latest versions of manuscripts available at http://physuna.phs.uc.edu/professors/serota.html or by e-mail, by request from [email protected]

Superconductor-proximity effect in chaotic and integrable billiards

We explore the effects of the proximity to a superconductor on the level density of a billiard for the two extreme cases that the classical motion in the billiard is chaotic or integrable. In zero magnetic field and for a uniform phase in the superconductor, a chaotic billiard has an excitation gap equal to the Thouless energy. In contrast, an integrable (rectangular or circular) billiard has a reduced density of states near the Fermi level, but no gap. We present numerical calculations for both cases in support of our analytical results. For the chaotic case, we calculate how the gap closes as a function of magnetic field or phase difference.Comment: 4 pages, RevTeX, 2 Encapsulated Postscript figures. To be published by Physica Scripta in the proceedings of the "17th Nordic Semiconductor Meeting", held in Trondheim, June 199

Evidence for the Validity of the Berry-Robnik Surmise in a Periodically Pulsed Spin System

We study the statistical properties of the spectrum of a quantum dynamical system whose classical counterpart has a mixed phase space structure consisting of two regular regions separated by a chaotical one. We make use of a simple symmetry of the system to separate the eigenstates of the time-evolution operator into two classes in agreement with the Percival classification scheme \cite{Per}. We then use a method firstly developed by Bohigas et. al. \cite{BoUlTo} to evaluate the fractional measure of states belonging to the regular class, and finally present the level spacings statistics for each class which confirm the validity of the Berry-Robnik surmise in our model.Comment: 15 pages, 9 figures available upon request, Latex fil

On the Accuracy of the Semiclassical Trace Formula

The semiclassical trace formula provides the basic construction from which one derives the semiclassical approximation for the spectrum of quantum systems which are chaotic in the classical limit. When the dimensionality of the system increases, the mean level spacing decreases as $\hbar^d$, while the semiclassical approximation is commonly believed to provide an accuracy of order $\hbar^2$, independently of d. If this were true, the semiclassical trace formula would be limited to systems in d <= 2 only. In the present work we set about to define proper measures of the semiclassical spectral accuracy, and to propose theoretical and numerical evidence to the effect that the semiclassical accuracy, measured in units of the mean level spacing, depends only weakly (if at all) on the dimensionality. Detailed and thorough numerical tests were performed for the Sinai billiard in 2 and 3 dimensions, substantiating the theoretical arguments.Comment: LaTeX, 31 pages, 14 figures, final version (minor changes

Early Advanced LIGO binary neutron-star sky localization and parameter estimation

2015 will see the first observations of Advanced LIGO and the start of the gravitational-wave (GW) advanced-detector era. One of the most promising sources for ground-based GW detectors are binary neutron-star (BNS) coalescences. In order to use any detections for astrophysics, we must understand the capabilities of our parameter-estimation analysis. By simulating the GWs from an astrophysically motivated population of BNSs, we examine the accuracy of parameter inferences in the early advanced-detector era. We find that sky location, which is important for electromagnetic follow-up, can be determined rapidly (~5 s), but that sky areas may be hundreds of square degrees. The degeneracy between component mass and spin means there is significant uncertainty for measurements of the individual masses and spins; however, the chirp mass is well measured (typically better than 0.1%).Comment: 4 pages, 2 figures. Published in the proceedings of Amaldi 1

Negative moments of characteristic polynomials of random GOE matrices and singularity-dominated strong fluctuations

We calculate the negative integer moments of the (regularized) characteristic polynomials of N x N random matrices taken from the Gaussian Orthogonal Ensemble (GOE) in the limit as $N \to \infty$. The results agree nontrivially with a recent conjecture of Berry & Keating motivated by techniques developed in the theory of singularity-dominated strong fluctuations. This is the first example where nontrivial predictions obtained using these techniques have been proved.Comment: 13 page