Extension of a Spectral Bounding Method to Complex Rotated Hamiltonians, with Application to p2−ix3p^2-ix^3

We show that a recently developed method for generating bounds for the discrete energy states of the non-hermitian $-ix^3$ potential (Handy 2001) is applicable to complex rotated versions of the Hamiltonian. This has important implications for extension of the method in the analysis of resonant states, Regge poles, and general bound states in the complex plane (Bender and Boettcher (1998)).Comment: Submitted to J. Phys.

Generating Converging Bounds to the (Complex) Discrete States of the P2+iX3+iαXP^2 + iX^3 + i\alpha X Hamiltonian

The Eigenvalue Moment Method (EMM), Handy (2001), Handy and Wang (2001)) is applied to the $H_\alpha \equiv P^2 + iX^3 + i\alpha X$ Hamiltonian, enabling the algebraic/numerical generation of converging bounds to the complex energies of the $L^2$ states, as argued (through asymptotic methods) by Delabaere and Trinh (J. Phys. A: Math. Gen. {\bf 33} 8771 (2000)).Comment: Submitted to J. Phys.

Eigenvalues of PT-symmetric oscillators with polynomial potentials

We study the eigenvalue problem $-u^{\prime\prime}(z)-[(iz)^m+P_{m-1}(iz)]u(z)=\lambda u(z)$ with the boundary conditions that $u(z)$ decays to zero as $z$ tends to infinity along the rays $\arg z=-\frac{\pi}{2}\pm \frac{2\pi}{m+2}$, where $P_{m-1}(z)=a_1 z^{m-1}+a_2 z^{m-2}+...+a_{m-1} z$ is a polynomial and integers $m\geq 3$. We provide an asymptotic expansion of the eigenvalues $\lambda_n$ as $n\to+\infty$, and prove that for each {\it real} polynomial $P_{m-1}$, the eigenvalues are all real and positive, with only finitely many exceptions.Comment: 23 pages, 1 figure. v2: equation (14) as well as a few subsequent equations has been changed. v3: typos correcte

Generating Converging Eigenenergy Bounds for the Discrete States of the -ix^3 Non-Hermitian Potential

Recent investigations by Bender and Boettcher (Phys. Rev. Lett 80, 5243 (1998)) and Mezincescu (J. Phys. A. 33, 4911 (2000)) have argued that the discrete spectrum of the non-hermitian potential $V(x) = -ix^3$ should be real. We give further evidence for this through a novel formulation which transforms the general one dimensional Schrodinger equation (with complex potential) into a fourth order linear differential equation for $|\Psi(x)|^2$. This permits the application of the Eigenvalue Moment Method, developed by Handy, Bessis, and coworkers (Phys. Rev. Lett. 55, 931 (1985);60, 253 (1988a,b)), yielding rapidly converging lower and upper bounds to the low lying discrete state energies. We adapt this formalism to the pure imaginary cubic potential, generating tight bounds for the first five discrete state energy levels.Comment: Work to appear in J. Phys. A: Math & Ge

Dynamics of the solar chromosphere. V. High-frequency modulation in ultraviolet image sequences from TRACE

We search for signatures of high-frequency oscillations in the upper solar photosphere and low chromosphere in the context of acoustic heating of outer stellar atmospheres. We use ultraviolet image sequences of a quiet center-disk area from the Transition Region and Coronal Explorer (TRACE) mission which were taken with strict cadence regularity. The latter permits more reliable high-frequency diagnosis than in earlier work. Spatial Fourier power maps, spatially averaged coherence and phase-difference spectra, and spatio-temporal k-f decompositions all contain high-frequency features that at first sight seem of considerable intrinsic interest but actually are more likely to represent artifacts of different nature. Spatially averaged phase difference measurement provides the most sensitive diagnostic and indicates the presence of acoustic modulation up to f=20 mHz (periods down to 50 seconds) in internetwork areas.Comment: 9 pages, 8 figure

Dynamic fibrils in H-alpha and C IV

Aim: To study the interaction of the solar chromosphere with the transition region, in particular active-region jets in the transition region and their relation to chromospheric fibrils. Methods: We carefully align image sequences taken simultaneously in C IV with the Transition Region and Coronal Explorer and in H-alpha with the Swedish 1-m Solar Telescope. We examine the temporal evolution of "dynamic fibrils", i.e., individual short-lived active-region chromospheric jet-like features in H-alpha. Results: All dynamic fibrils appear as absorption features in H-alpha that progress from the blue to the red wing through the line, and often show recurrent behavior. Some of them, but not all, appear also as bright features in C IV which develop at or just beyond the apex of the H-alpha darkening. They tend to best resemble the H-alpha fibril at +700 mA half a minute earlier. Conclusions: Dynamic chromospheric fibrils observed in H-alpha regularly correspond to transition-region jets observed in the ultraviolet. This correspondence suggests that some plasma associated with dynamic fibrils is heated to transition-region temperatures.Comment: 8 pages, 8 figure

Distributed leadership, trust and online communities

This paper analyses the role of distributed leadership and trust in online communities. The team-based informal ethos of online collaboration requires a different kind of leadership from that in formal positional hierarchies. Such leadership may be more flexible and sophisticated, capable of encompassing ambiguity and rapid change. Online leaders need to be partially invisible, delegating power and distributing tasks. Yet, simultaneously, online communities are facilitated by the high visibility and subtle control of expert leaders. This paradox: that leaders need to be both highly visible and invisible as appropriate, was derived from prior research and tested in the analysis of online community discussions using a pattern-matching process. It is argued that both leader visibility and invisibility are important for the facilitation of trusting collaboration via distributed leadership. Advanced leadership responses to complex situations in online communities foster positive group interaction and decision-making, facilitated through active distribution of specific tasks

On the uniqueness of the surface sources of evoked potentials

The uniqueness of a surface density of sources localized inside a spatial region $R$ and producing a given electric potential distribution in its boundary $B_0$ is revisited. The situation in which $R$ is filled with various metallic subregions, each one having a definite constant value for the electric conductivity is considered. It is argued that the knowledge of the potential in all $B_0$ fully determines the surface density of sources over a wide class of surfaces supporting them. The class can be defined as a union of an arbitrary but finite number of open or closed surfaces. The only restriction upon them is that no one of the closed surfaces contains inside it another (nesting) of the closed or open surfaces.Comment: 16 pages, 5 figure