2,700 research outputs found
Extension of a Spectral Bounding Method to Complex Rotated Hamiltonians, with Application to
We show that a recently developed method for generating bounds for the
discrete energy states of the non-hermitian 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 Hamiltonian
The Eigenvalue Moment Method (EMM), Handy (2001), Handy and Wang (2001)) is
applied to the Hamiltonian, enabling
the algebraic/numerical generation of converging bounds to the complex energies
of the 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
with the boundary
conditions that decays to zero as tends to infinity along the rays
, where is a polynomial and integers . We provide an
asymptotic expansion of the eigenvalues as , and prove
that for each {\it real} polynomial , 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 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 . 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 and producing a given electric potential distribution in its
boundary is revisited. The situation in which 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 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
1958 Ohio Farm Income: Estimated Cash Receipts From Farm Marketing and Government Payments, by Counties and Major Commodity Groups
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