Nodal domain distributions for quantum maps

The statistics of the nodal lines and nodal domains of the eigenfunctions of quantum billiards have recently been observed to be fingerprints of the chaoticity of the underlying classical motion by Blum et al. (Phys. Rev. Lett., Vol. 88 (2002), 114101) and by Bogomolny and Schmit (Phys. Rev. Lett., Vol. 88 (2002), 114102). These statistics were shown to be computable from the random wave model of the eigenfunctions. We here study the analogous problem for chaotic maps whose phase space is the two-torus. We show that the distributions of the numbers of nodal points and nodal domains of the eigenvectors of the corresponding quantum maps can be computed straightforwardly and exactly using random matrix theory. We compare the predictions with the results of numerical computations involving quantum perturbed cat maps.Comment: 7 pages, 2 figures. Second version: minor correction

Investigating the Structure of the Windy Torus in Quasars

Thermal mid-infrared emission of quasars requires an obscuring structure that can be modeled as a magneto-hydrodynamic wind in which radiation pressure on dust shapes the outflow. We have taken the dusty wind models presented by Keating and collaborators that generated quasar mid-infrared spectral energy distributions (SEDs), and explored their properties (such as geometry, opening angle, and ionic column densities) as a function of Eddington ratio and X-ray weakness. In addition, we present new models with a range of magnetic field strengths and column densities of the dust-free shielding gas interior to the dusty wind. We find this family of models -- with input parameters tuned to accurately match the observed mid-IR power in quasar SEDs -- provides reasonable values of the Type 1 fraction of quasars and the column densities of warm absorber gas, though it does not explain a purely luminosity-dependent covering fraction for either. Furthermore, we provide predictions of the cumulative distribution of E(B-V) values of quasars from extinction by the wind and the shape of the wind as imaged in the mid-infrared. Within the framework of this model, we predict that the strength of the near-infrared bump from hot dust emission will be correlated primarily with L/L_Edd rather than luminosity alone, with scatter induced by the distribution of magnetic field strengths. The empirical successes and shortcomings of these models warrant further investigations into the composition and behaviour of dust and the nature of magnetic fields in the vicinity of actively accreting supermassive black holes.Comment: 11 pages, 6 figures, accepted for publication in MNRA

Nodal Domain Statistics for Quantum Maps, Percolation and SLE

We develop a percolation model for nodal domains in the eigenvectors of quantum chaotic torus maps. Our model follows directly from the assumption that the quantum maps are described by random matrix theory. Its accuracy in predicting statistical properties of the nodal domains is demonstrated by numerical computations for perturbed cat maps and supports the use of percolation theory to describe the wave functions of general hamiltonian systems, where the validity of the underlying assumptions is much less clear. We also demonstrate that the nodal domains of the perturbed cat maps obey the Cardy crossing formula and find evidence that the boundaries of the nodal domains are described by SLE with $\kappa$ close to the expected value of 6, suggesting that quantum chaotic wave functions may exhibit conformal invariance in the semiclassical limit.Comment: 4 pages, 5 figure

Design of a Flight Controller for an Unmanned Research Vehicle with Control Surface Failures Using Quantitative Feedback Theory

This thesis describes the application of the multiple-input multiple- output (MIMO) Quantitative Feedback Theory (QFT) design technique to the design of a digital flight control system for the Lambda Unmanned Research Vehicle (URV). The QFT technique allows the synthesis of a control system which is robust in the presence of structured plant uncertainties. Uncertainties considered in this design are the aircraft\u27s plant variation within the flight envelope and the effects of damage to aircraft control surfaces. Mathematical models of control surface failure effects on aircraft dynamics are derived and used to modify an existing small perturbation model of the Lambda. The QFT technique is applied to design a control system utilizing aircraft pitch rate, roll rate and sideslip angle as feedback variables. The inherent cross-coupling rejection qualities of QFT and an aileron-rudder interconnect are utilized to design a control system which results in a coordinated flight. An outer-loop autopilot is then designed around the QFT controller to further assist turn coordination. Sensor noise effects on aircraft states are also analyzed. Quantitative feedback theory, Flight control system, Aircraft damage

Assessing Financial Vulnerability in the Nonprofit Sector

Effective nonprofit governance relies upon understanding an organization's financial condition and vulnerabilities. However, financial vulnerability of nonprofit organizations is a relatively new area of study. In this paper, we compare two models used to forecast bankruptcy in the corporate sector (Altman 1968 and Ohlson 1980) with the model used by nonprofit researchers (Tuckman and Chang 1991). We find that the Ohlson model has higher explanatory power than either Tuckman and Chang's or Altman's in predicting four different measures of financial vulnerability. However, we show that none of the models, individually or combined, are effective in predicting financial distress. We then propose a more comprehensive model of financial vulnerability by adding two new variables to represent reliance on commercial-type activities to generate revenues and endowment sufficiency. We find that this model outperforms Ohlson's model and performs substantially better in explaining and predicting financial vulnerability. Hence, the expanded model can be used as a guide for understanding the drivers of financial vulnerability and for identifying more effective proxies for nonprofit sector financial distress for use in future research. This publication is Hauser Center Working Paper No. 27. The Hauser Center Working Paper Series was launched during the summer of 2000. The Series enables the Hauser Center to share with a broad audience important works-in-progress written by Hauser Center scholars and researchers

Fractional ℏ\hbar-scaling for quantum kicked rotors without cantori

Previous studies of quantum delta-kicked rotors have found momentum probability distributions with a typical width (localization length $L$) characterized by fractional $\hbar$-scaling, ie $L \sim \hbar^{2/3}$ in regimes and phase-space regions close to `golden-ratio' cantori. In contrast, in typical chaotic regimes, the scaling is integer, $L \sim \hbar^{-1}$. Here we consider a generic variant of the kicked rotor, the random-pair-kicked particle (RP-KP), obtained by randomizing the phases every second kick; it has no KAM mixed phase-space structures, like golden-ratio cantori, at all. Our unexpected finding is that, over comparable phase-space regions, it also has fractional scaling, but $L \sim \hbar^{-2/3}$. A semiclassical analysis indicates that the $\hbar^{2/3}$ scaling here is of quantum origin and is not a signature of classical cantori.Comment: 5 pages, 4 figures, Revtex, typos removed, further analysis added, authors adjuste

On the resonance eigenstates of an open quantum baker map

We study the resonance eigenstates of a particular quantization of the open baker map. For any admissible value of Planck's constant, the corresponding quantum map is a subunitary matrix, and the nonzero component of its spectrum is contained inside an annulus in the complex plane, $|z_{min}|\leq |z|\leq |z_{max}|$. We consider semiclassical sequences of eigenstates, such that the moduli of their eigenvalues converge to a fixed radius $r$. We prove that, if the moduli converge to $r=|z_{max}|$, then the sequence of eigenstates converges to a fixed phase space measure $\rho_{max}$. The same holds for sequences with eigenvalue moduli converging to $|z_{min}|$, with a different limit measure $\rho_{min}$. Both these limiting measures are supported on fractal sets, which are trapped sets of the classical dynamics. For a general radius $|z_{min}|< r < |z_{max}|$, we identify families of eigenstates with precise self-similar properties.Comment: 32 pages, 2 figure