11,852 research outputs found
Eigenvalue Integro-Differential Equations for Orthogonal Polynomials on the Real Line
The one-dimensional harmonic oscillator wave functions are solutions to a
Sturm-Liouville problem posed on the whole real line. This problem generates
the Hermite polynomials. However, no other set of orthogonal polynomials can be
obtained from a Sturm-Liouville problem on the whole real line. In this paper
we show how to characterize an arbitrary set of polynomials orthogonal on
in terms of a system of integro-differential equations of
Hartree-Fock type. This system replaces and generalizes the linear differential
equation associated with a Sturm-Liouville problem. We demonstrate our results
for the special case of Hahn-Meixner polynomials.Comment: 28 pages, Latex, U. Texas at Austin/ Washington University preprin
Vector Casimir effect for a D-dimensional sphere
The Casimir energy or stress due to modes in a D-dimensional volume subject
to TM (mixed) boundary conditions on a bounding spherical surface is
calculated. Both interior and exterior modes are included. Together with
earlier results found for scalar modes (TE modes), this gives the Casimir
effect for fluctuating ``electromagnetic'' (vector) fields inside and outside a
spherical shell. Known results for three dimensions, first found by Boyer, are
reproduced. Qualitatively, the results for TM modes are similar to those for
scalar modes: Poles occur in the stress at positive even dimensions, and cusps
(logarithmic singularities) occur for integer dimensions . Particular
attention is given the interesting case of D=2.Comment: 20 pages, 1 figure, REVTe
Harmonic oscillator well with a screened Coulombic core is quasi-exactly solvable
In the quantization scheme which weakens the hermiticity of a Hamiltonian to
its mere PT invariance the superposition V(x) = x^2+ Ze^2/x of the harmonic and
Coulomb potentials is defined at the purely imaginary effective charges
(Ze^2=if) and regularized by a purely imaginary shift of x. This model is
quasi-exactly solvable: We show that at each excited, (N+1)-st
harmonic-oscillator energy E=2N+3 there exists not only the well known harmonic
oscillator bound state (at the vanishing charge f=0) but also a normalizable
(N+1)-plet of the further elementary Sturmian eigenstates \psi_n(x) at
eigencharges f=f_n > 0, n = 0, 1, ..., N. Beyond the first few smallest
multiplicities N we recommend their perturbative construction.Comment: 13 pages, Latex file, to appear in J. Phys. A: Math. Ge
Does the complex deformation of the Riemann equation exhibit shocks?
The Riemann equation , which describes a one-dimensional
accelerationless perfect fluid, possesses solutions that typically develop
shocks in a finite time. This equation is \cP\cT symmetric. A one-parameter
\cP\cT-invariant complex deformation of this equation,
( real), is solved exactly using the
method of characteristic strips, and it is shown that for real initial
conditions, shocks cannot develop unless is an odd integer.Comment: latex, 8 page
An SCF-stabilization approach to excited states embedded in the continuum
By using SCF and stabilization‐like procedures, we have located a (π, π*) singlet resonance‐like state in ethylene at 10.21 eV. This state is embedded in the ionization continuum and carries an oscillator strength of 0.46 and is probably the analog to the spectroscopic V state in Hartree–Fock theory. Implications of these results for other systems are discussed
On the eigenproblems of PT-symmetric oscillators
We consider the non-Hermitian Hamiltonian H=
-\frac{d^2}{dx^2}+P(x^2)-(ix)^{2n+1} on the real line, where P(x) is a
polynomial of degree at most n \geq 1 with all nonnegative real coefficients
(possibly P\equiv 0). It is proved that the eigenvalues \lambda must be in the
sector | arg \lambda | \leq \frac{\pi}{2n+3}. Also for the case
H=-\frac{d^2}{dx^2}-(ix)^3, we establish a zero-free region of the
eigenfunction u and its derivative u^\prime and we find some other interesting
properties of eigenfunctions.Comment: 21pages, 9 figure
Chaotic systems in complex phase space
This paper examines numerically the complex classical trajectories of the
kicked rotor and the double pendulum. Both of these systems exhibit a
transition to chaos, and this feature is studied in complex phase space.
Additionally, it is shown that the short-time and long-time behaviors of these
two PT-symmetric dynamical models in complex phase space exhibit strong
qualitative similarities.Comment: 22 page, 16 figure
Twins Among the Low Mass Spectroscopic Binaries
We report an analysis of twins of spectral types F or later in the 9th
Catalog of Spectroscopic Binaries (SB9). Twins, the components of binaries with
mass ratio within 2% of 1.0, are found among the binaries with primaries of F
and G spectral type. They are most prominent among the binaries with periods
less than 43 days, a cutoff first identified by Lucy. Within the subsample of
binaries with P<43 days, the twins do not differ from the other binaries in
their distributions of periods (median P~7d), masses, or orbital
eccentricities. Combining the mass ratio distribution in the SB9 in the mass
range 0.6 to 0.85 Msun with that measured by Mazeh et al. for binaries in the
Carney-Latham high proper motion survey, we estimate that the frequency of
twins in a large sample of spectroscopic binaries is about 3%. Current
theoretical understanding indicates that accretion of high specific angular
momentum material by a protobinary tends to equalize its masses. We speculate
that the excess of twins is produced in those star forming regions where the
accretion processes were able to proceed to completion for a minority of
protobinaries. This predicts that the components of a young twin may appear to
differ in age and that, in a sample of spectroscopic binaries in a star
formation region, the twins are, on average, older than the binaries with mass
ratios much smaller than 1.Comment: Accepted by the Astronomical Journa
Addendum to SSV Generic OFT First Stage Ascent Base Convective Heating Environments
Convective environments for OFT Mission C are presented in graphs for first stage convective heating to the internal surfaces of the OMS nozzle, to the aft facing 8 and 9 RCS nozzles, and to the base (trailing edge) of the vertical tail
The Isophotal Structure of Early-Type Galaxies in the SDSS: Dependence on AGN Activity and Environment
We study the dependence of the isophotal shape of early-type galaxies on
their absolute B-band magnitude, their dynamical mass, and their nuclear
activity and environment, using an unprecedented large sample of 847 early-type
galaxies identified in the SDSS by Hao et al (2006). We find that the fraction
of disky galaxies smoothly decreases with increasing luminosity. The large
sample allows us to describe these trends accurately with tight linear
relations that are statistically robust against the uncertainty in the
isophotal shape measurements. There is also a host of significant correlations
between the disky fraction and indicators of nuclear activity (both in the
optical and in the radio) and environment (soft X-rays, group mass, group
hierarchy). Our analysis shows however that these correlations can be
accurately matched by assuming that the disky fraction depends only on galaxy
luminosity or mass. We therefore conclude that neither the level of activity,
nor group mass or group hierarchy help in better predicting the isophotal shape
of early-type galaxies.Comment: 31 pages, 10 figures, accepted for publication in Ap
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