Wave Propagation in Gravitational Systems: Completeness of Quasinormal Modes

The dynamics of relativistic stars and black holes are often studied in terms of the quasinormal modes (QNM's) of the Klein-Gordon (KG) equation with different effective potentials $V(x)$. In this paper we present a systematic study of the relation between the structure of the QNM's of the KG equation and the form of $V(x)$. In particular, we determine the requirements on $V(x)$ in order for the QNM's to form complete sets, and discuss in what sense they form complete sets. Among other implications, this study opens up the possibility of using QNM expansions to analyse the behavior of waves in relativistic systems, even for systems whose QNM's do {\it not} form a complete set. For such systems, we show that a complete set of QNM's can often be obtained by introducing an infinitesimal change in the effective potential

Perturbative Approach to the Quasinormal Modes of Dirty Black Holes

Using a recently developed perturbation theory for uasinormal modes (QNM's), we evaluate the shifts in the real and imaginary parts of the QNM frequencies due to a quasi-static perturbation of the black hole spacetime. We show the perturbed QNM spectrum of a black hole can have interesting features using a simple model based on the scalar wave equation.Comment: Published in PR

Quasi-Normal Mode Expansion for Linearized Waves in Gravitational Systems

The quasinormal modes (QNM's) of gravitational systems modeled by the Klein-Gordon equation with effective potentials are studied in analogy to the QNM's of optical cavities. Conditions are given for the QNM's to form a complete set, i.e., for the Green's function to be expressible as a sum over QNM's, answering a conjecture by Price and Husain [Phys. Rev. Lett. {\bf 68}, 1973 (1992)]. In the cases where the QNM sum is divergent, procedures for regularization are given. The crucial condition for completeness is the existence of spatial discontinuities in the system, e.g., the discontinuity at the stellar surface in the model of Price and Husain.Comment: 12 pages, WUGRAV-94-

Extraction of Coupling Information From Z′→jjZ' \to jj

An analysis by the ATLAS Collaboration has recently shown, contrary to popular belief, that a combination of strategic cuts, excellent mass resolution, and detailed knowledge of the QCD backgrounds from direct measurements can be used to extract a signal in the $Z' \to jj$ channel in excess of $6\sigma$ for certain classes of extended electroweak models. We explore the possibility that the data extracted from $Z$ dijet peak will have sufficient statistical power as to supply information on the couplings of the $Z'$ provided it is used in conjunction with complimentary results from the $Z' \to \ell^+ \ell^-$ `discovery' channel. We show, for a 1 TeV $Z'$ produced at the SSC, that this technique can provide a powerful new tool with which to identify the origin of $Z'$'s.Comment: 24 pages, 9 figures(available on request), LaTex, ANL-HEP-PR-93-1

Eigenvector Expansion and Petermann Factor for Ohmically Damped Oscillators

Correlation functions $C(t) \sim$ in ohmically damped systems such as coupled harmonic oscillators or optical resonators can be expressed as a single sum over modes $j$ (which are not power-orthogonal), with each term multiplied by the Petermann factor (PF) $C_j$, leading to "excess noise" when $|C_j| > 1$. It is shown that $|C_j| > 1$ is common rather than exceptional, that $|C_j|$ can be large even for weak damping, and that the PF appears in other processes as well: for example, a time-independent perturbation \sim\ep leads to a frequency shift \sim \ep C_j. The coalescence of $J$ ($>1$) eigenvectors gives rise to a critical point, which exhibits "giant excess noise" ($C_j \to \infty$). At critical points, the divergent parts of $J$ contributions to $C(t)$ cancel, while time-independent perturbations lead to non-analytic shifts \sim \ep^{1/J}.Comment: REVTeX4, 14 pages, 4 figures. v2: final, 20 single-col. pages, 2 figures. Streamlined with emphasis on physics over formalism; rewrote Section V E so that it refers to time-dependent (instead of non-equilibrium) effect

Is the particle current a relevant feature in driven lattice gases?

By performing extensive MonteCarlo simulations we show that the infinitely fast driven lattice gas (IDLG) shares its critical properties with the randomly driven lattice gas (RDLG). All the measured exponents, scaling functions and amplitudes are the same in both cases. This strongly supports the idea that the main relevant non-equilibrium effect in driven lattice gases is the anisotropy (present in both IDLG and RDLG) and not the particle current (present only in the IDLG). This result, at odds with the predictions from the standard theory for the IDLG, supports a recently proposed alternative theory. The case of finite driving fields is also briefly discussed.Comment: 4 pages. Slightly improved version. Journal Reference: To appear in Phys. Rev. Let

Fabrication of bismuth nanowires with a silver nanocrystal shadowmask

We fabricated bismuth (Bi) nanowires with low energy electron beam lithography using silver (Ag) nanocrystal shadowmasks and a subsequent chlorine reactive ion etching. Submicron-size metal contacts on the single Bi nanowire were successfully prepared by in situ focused ion beam metal deposition for transport measurements. The temperature dependent resistance measurements on the 50 nm wide Bi nanowires showed that the resistance increased with decreasing temperature, which is characteristic of semiconductors and insulators

Modeling esophageal protection from radiofrequency ablation via a cooling device: an analysis of the effects of ablation power and heart wall dimensions.

BACKGROUND: Esophageal thermal injury can occur after radiofrequency (RF) ablation in the left atrium to treat atrial fibrillation. Existing methods to prevent esophageal injury have various limitations in deployment and uncertainty in efficacy. A new esophageal heat transfer device currently available for whole-body cooling or warming may offer an additional option to prevent esophageal injury. We sought to develop a mathematical model of this process to guide further studies and clinical investigations and compare results to real-world clinical data. RESULTS: The model predicts that the esophageal cooling device, even with body-temperature water flow (37 °C) provides a reduction in esophageal thermal injury compared to the case of the non-protected esophagus, with a non-linear direct relationship between lesion depth and the cooling water temperature. Ablation power and cooling water temperature have a significant influence on the peak temperature and the esophageal lesion depth, but even at high RF power up to 50 W, over durations up to 20 s, the cooling device can reduce thermal impact on the esophagus. The model concurs with recent clinical data showing an 83% reduction in transmural thermal injury when using typical operating parameters. CONCLUSIONS: An esophageal cooling device appears effective for esophageal protection during atrial fibrillation, with model output supporting clinical data. Analysis of the impact of ablation power and heart wall dimensions suggests that cooling water temperature can be adjusted for specific ablation parameters to assure the desired myocardial tissue ablation while keeping the esophagus protected

Dynamic behavior of anisotropic non-equilibrium driving lattice gases

It is shown that intrinsically anisotropic non-equilibrium systems relaxing by a dynamic process exhibit universal critical behavior during their evolution toward non-equilibrium stationary states. An anisotropic scaling anzats for the dynamics is proposed and tested numerically. Relevant critical exponents can be evaluated self-consistently using both the short- and long-time dynamics frameworks. The obtained results allow us to clarify a long-standing controversy about the theoretical description, the universality and the origin of the anisotropy of driven diffusive systems, showing that the standard field theory does not hold and supporting a recently proposed alternative theory.Comment: 4 pages, 2 figure

Unconventional Gravitational Excitation of a Schwarzschild Black Hole

Besides the well-known quasinormal modes, the gravitational spectrum of a Schwarzschild black hole also has a continuum part on the negative imaginary frequency axis. The latter is studied numerically for quadrupole waves. The results show unexpected striking behavior near the algebraically special frequency $\Omega=-4i$. This reveals a pair of unconventional damped modes very near $\Omega$, confirmed analytically.Comment: REVTeX4, 4pp, 6 EPS figure files. N.B.: "Alec" is my first, and "Maassen van den Brink" my family name. v2: better pole placement in Fig. 1. v3: fixed Refs. [9,20]. v4: added context on "area quantum" research; trimmed one Fig.; textual clarification