22,743 research outputs found
Analytic structure of Bloch functions for linear molecular chains
This paper deals with Hamiltonians of the form H=-{\bf \nabla}^2+v(\rr),
with v(\rr) periodic along the direction, . The
wavefunctions of are the well known Bloch functions
\psi_{n,\lambda}(\rr), with the fundamental property
and
. We give the generic analytic structure
(i.e. the Riemann surface) of \psi_{n,\lambda}(\rr) and their corresponding
energy, , as functions of . We show that
and are different branches of two multi-valued
analytic functions, and , with an essential
singularity at and additional branch points, which are generically
of order 1 and 3, respectively. We show where these branch points come from,
how they move when we change the potential and how to estimate their location.
Based on these results, we give two applications: a compact expression of the
Green's function and a discussion of the asymptotic behavior of the density
matrix for insulating molecular chains.Comment: 13 pages, 11 figure
On the convergence of second order spectra and multiplicity
Let A be a self-adjoint operator acting on a Hilbert space. The notion of
second order spectrum of A relative to a given finite-dimensional subspace L
has been studied recently in connection with the phenomenon of spectral
pollution in the Galerkin method. We establish in this paper a general
framework allowing us to determine how the second order spectrum encodes
precise information about the multiplicity of the isolated eigenvalues of A.
Our theoretical findings are supported by various numerical experiments on the
computation of inclusions for eigenvalues of benchmark differential operators
via finite element bases.Comment: 22 pages, 2 figures, 4 tables, research paper
Spectral analysis of temperature and Brunt-Vaisala frequency fluctuations observed by radiosondes
Recent studies have revealed that vertical wave number spectra of wind velocity and temperture fluctuations in the troposphere and the lower stratosphere are fairly well explained by a saturated gravity wave spectrum. But N(2) (N:Brunt-Vaisala (BV) frequency) spectra seem to be better for testing the scaling of the vertical wave number spectra in layers with different stratifications, beause its energy density is proportional only to the background value of N(2), while that for temperature depends on both the BV frequency and the potential temperature. From temperature profiles observed in June to August 1987 over the MU Observatory, Japan, by using a radiosonde with 30 m height resolution, N(2) spectra are determined in the 2 to 8.5 km (troposphere) and 18.5 to 25 km (lower stratosphere) ranges. Although individual spectra show fairly large day-by-day variability, the slope of the median of 34 spectra agrees reasonably with the theoretical value of -1 in the wave number range of 6 x 10(-4) similar to 3 x 10(-3) (c/m). The ratio of the spectral energy between these two height regions is about equal to the ratio of N(2), consistent with the prediction of saturated gravity wave theory
PT-Symmetric Sinusoidal Optical Lattices at the Symmetry-Breaking Threshold
The symmetric potential has
a completely real spectrum for , and begins to develop complex
eigenvalues for . At the symmetry-breaking threshold
some of the eigenvectors become degenerate, giving rise to a Jordan-block
structure for each degenerate eigenvector. In general this is expected to
result in a secular growth in the amplitude of the wave. However, it has been
shown in a recent paper by Longhi, by numerical simulation and by the use of
perturbation theory, that for a broad initial wave packet this growth is
suppressed, and instead a saturation leading to a constant maximum amplitude is
observed. We revisit this problem by explicitly constructing the Bloch
wave-functions and the associated Jordan functions and using the method of
stationary states to find the dependence on the longitudinal distance for a
variety of different initial wave packets. This allows us to show in detail how
the saturation of the linear growth arises from the close connection between
the contributions of the Jordan functions and those of the neighbouring Bloch
waves.Comment: 15 pages, 7 figures Minor corrections, additional reference
Analycity and smoothing effect for the coupled system of equations of Korteweg - de Vries type with a single point singularity
We study that a solution of the initial value problem associated for the
coupled system of equations of Korteweg - de Vries type which appears as a
model to describe the strong interaction of weakly nonlinear long waves, has
analyticity in time and smoothing effect up to real analyticity if the initial
data only has a single point singularity at $x=0.
Adjointness Relations as a Criterion for Choosing an Inner Product
This is a contribution to the forthcoming book "Canonical Gravity: {}From
Classical to Quantum" edited by J. Ehlers and H. Friedrich. Ashtekar's
criterion for choosing an inner product in the quantisation of constrained
systems is discussed. An erroneous claim in a previous paper is corrected and a
cautionary example is presented.Comment: 6 pages, MPA-AR-94-
Asteroseismological Observations of the Central Star of the Planetary Nebula NGC 1501
We report on a global CCD time-series photometric campaign to decode the
pulsations of the nucleus of the planetary nebula NGC1501. The star is hot and
hydrogen-deficient, similar to the pre-white-dwarf PG 1159 stars. NGC1501 shows
pulsational brightness variations of a few percent with periods ranging from 19
to 87 minutes. The variations are very complex, suggesting a pulsation spectrum
that requires a long unbroken time series to resolve. Our CCD photometry of the
star covers a two-week period in 1991 November, and used a global network of
observatories. We obtained nearly continuous coverage over an interval of one
week in the middle of the run. We have identified 10 pulsation periods, ranging
from 5235 s down to 1154 s. We find strong evidence that the modes are indeed
nonradial g-modes. The ratios of the frequencies of the largest-amplitude modes
agree with those expected for modes that are trapped by a density discontinuity
in the outer layers. We offer a model for the pulsation spectrum that includes
a common period spacing of 22.3 s and a rotation period of 1.17 days; the
period spacing allows us to assign a seismological mass of 0.55+/-0.03 Msun.Comment: 12 pages, AASTEX, 7 tables, 6 EPS figures, to appear in AJ, 12/96
Corrected version repairs table formatting and adds missing Table
In-the-Gap SU UMa-Type Dwarf Nova, Var73 Dra with a Supercycle of about 60 Days
An intensive photometric-observation campaign of the recently discovered SU
UMa-type dwarf nova, Var73 Dra was conducted from 2002 August to 2003 February.
We caught three superoutbursts in 2002 October, December and 2003 February. The
recurrence cycle of the superoutburst (supercycle) is indicated to be 60
d, the shortest among the values known so far in SU UMa stars and close to
those of ER UMa stars. The superhump periods measured during the first two
superoutbursts were 0.104885(93) d, and 0.10623(16) d, respectively. A
0.10424(3)-d periodicity was detected in quiescence. The change rate of the
superhump period during the second superoutburst was , which
is an order of magnitude larger than the largest value ever known. Outburst
activity has changed from a phase of frequent normal outbursts and infrequent
superoutbursts in 2001 to a phase of infrequent normal outbursts and frequent
superoutbursts in 2002. Our observations are negative to an idea that this star
is an related object to ER UMa stars in terms of the duty cycle of the
superoutburst and the recurrence cycle of the normal outburst. However, to
trace the superhump evolution throughout a superoutburst, and from quiescence
more effectively, may give a fruitful result on this matter.Comment: 9 pages, 8 figures, submitted to A&
Ensemble averageability in network spectra
The extreme eigenvalues of connectivity matrices govern the influence of the
network structure on a number of network dynamical processes. A fundamental
open question is whether the eigenvalues of large networks are well represented
by ensemble averages. Here we investigate this question explicitly and validate
the concept of ensemble averageability in random scale-free networks by showing
that the ensemble distributions of extreme eigenvalues converge to peaked
distributions as the system size increases. We discuss the significance of this
result using synchronization and epidemic spreading as example processes.Comment: 4 pages, 4 figure
- …