6,598 research outputs found
Orbital Parameter Determination for Wide Stellar Binary Systems in the Age of Gaia
The orbits of binary stars and planets, particularly eccentricities and
inclinations, encode the angular momentum within these systems. Within stellar
multiple systems, the magnitude and (mis)alignment of angular momentum vectors
among stars, disks, and planets probes the complex dynamical processes guiding
their formation and evolution. The accuracy of the \textit{Gaia} catalog can be
exploited to enable comparison of binary orbits with known planet or disk
inclinations without costly long-term astrometric campaigns. We show that
\textit{Gaia} astrometry can place meaningful limits on orbital elements in
cases with reliable astrometry, and discuss metrics for assessing the
reliability of \textit{Gaia} DR2 solutions for orbit fitting. We demonstrate
our method by determining orbital elements for three systems (DS Tuc AB, GK/GI
Tau, and Kepler-25/KOI-1803) using \textit{Gaia} astrometry alone. We show that
DS Tuc AB's orbit is nearly aligned with the orbit of DS Tuc Ab, GK/GI Tau's
orbit might be misaligned with their respective protoplanetary disks, and the
Kepler-25/KOI-1803 orbit is not aligned with either component's transiting
planetary system. We also demonstrate cases where \textit{Gaia} astrometry
alone fails to provide useful constraints on orbital elements. To enable
broader application of this technique, we introduce the python tool
\texttt{lofti\_gaiaDR2} to allow users to easily determine orbital element
posteriors.Comment: 18 pages, 10 figures, accepted for publication in Ap
Levinson's Theorem for Non-local Interactions in Two Dimensions
In the light of the Sturm-Liouville theorem, the Levinson theorem for the
Schr\"{o}dinger equation with both local and non-local cylindrically symmetric
potentials is studied. It is proved that the two-dimensional Levinson theorem
holds for the case with both local and non-local cylindrically symmetric cutoff
potentials, which is not necessarily separable. In addition, the problems
related to the positive-energy bound states and the physically redundant state
are also discussed in this paper.Comment: Latex 11 pages, no figure, submitted to J. Phys. A Email:
[email protected], [email protected]
Enhanced observability of quantum post-exponential decay using distant detectors
We study the elusive transition from exponential to post-exponential
(algebraic) decay of the probability density of a quantum particle emitted by
an exponentially decaying source, in one dimension. The main finding is that
the probability density at the transition time, and thus its observability,
increases with the distance of the detector from the source, up to a critical
distance beyond which exponential decay is no longer observed. Solvable models
provide explicit expressions for the dependence of the transition on resonance
and observational parameters, facilitating the choice of optimal conditions
Pade approximation of the S-matrix as a way of locating quantum resonances and bound states
It is shown that the spectral points (bound states and resonances) generated
by a central potential of a single-channel problem, can be found using rational
parametrization of the S-matrix. To achieve this, one only needs values of the
S-matrix along the real positive energy axis. No calculations of the S-matrix
at complex energies or a complex rotation are necessary. The proposed method is
therefore universal in that it is applicable to any potential (local,
non-local, discontinuous, etc.) provided that there is a way of obtaining the
S-matrix (or scattering phase-shifts) at real collision energies. Besides this,
combined with any method that extracts the phase-shifts from the scattering
data, the proposed rational parametrization technique would be able to do the
spectral analysis using the experimental data.Comment: 20 pages, 6 figure
Reformulating the Schrodinger equation as a Shabat-Zakharov system
We reformulate the second-order Schrodinger equation as a set of two coupled
first order differential equations, a so-called "Shabat-Zakharov system",
(sometimes called a "Zakharov-Shabat" system). There is considerable
flexibility in this approach, and we emphasise the utility of introducing an
"auxiliary condition" or "gauge condition" that is used to cut down the degrees
of freedom. Using this formalism, we derive the explicit (but formal) general
solution to the Schrodinger equation. The general solution depends on three
arbitrarily chosen functions, and a path-ordered exponential matrix. If one
considers path ordering to be an "elementary" process, then this represents
complete quadrature, albeit formal, of the second-order linear ODE.Comment: 18 pages, plain LaTe
Antibound States and Halo Formation in the Gamow Shell Model
The open quantum system formulation of the nuclear shell model, the so-called
Gamow Shell Model (GSM), is a multi-configurational SM that employs a
single-particle basis given by the Berggren ensemble consisting of Gamow states
and the non-resonant continuum of scattering states. The GSM is of particular
importance for weakly bound/unbound nuclear states where both many-body
correlations and the coupling to decay channels are essential. In this context,
we investigate the role of l=0 antibound (virtual) neutron single-particle
states in the shell model description of loosely bound wave functions, such as
the ground state wave function of a halo nucleus 11Li
Poincare Semigroup Symmetry as an Emergent Property of Unstable Systems
The notion that elementary systems correspond to irreducible representations
of the Poincare group is the starting point for this paper, which then goes on
to discuss how a semigroup for the time evolution of unstable states and
resonances could emerge from the underlying Poincare symmetry. Important tools
in this analysis are the Clebsch-Gordan coefficients for the Poincare group.Comment: 17 pages, 1 figur
A possible mechanism of ultrafast amorphization in phase-change memory alloys: an ion slingshot from the crystalline to amorphous position
We propose that the driving force of an ultrafast crystalline-to-amorphous
transition in phase-change memory alloys are strained bonds existing in the
(metastable) crystalline phase. For the prototypical example of GST, we
demonstrate that upon breaking of long Ge-Te bond by photoexcitation Ge ion
shot from an octahedral crystalline to a tetrahedral amorphous position by the
uncompensated force of strained short bonds. Subsequent lattice relaxation
stabilizes the tetrahedral surroundings of the Ge atoms and ensures the
long-term stability of the optically induced phase.Comment: 6 pages, 3 figure
Nonlocal Electrodynamics of Rotating Systems
The nonlocal electrodynamics of uniformly rotating systems is presented and
its predictions are discussed. In this case, due to paucity of experimental
data, the nonlocal theory cannot be directly confronted with observation at
present. The approach adopted here is therefore based on the correspondence
principle: the nonrelativistic quantum physics of electrons in circular
"orbits" is studied. The helicity dependence of the photoeffect from the
circular states of atomic hydrogen is explored as well as the resonant
absorption of a photon by an electron in a circular "orbit" about a uniform
magnetic field. Qualitative agreement of the predictions of the classical
nonlocal electrodynamics with quantum-mechanical results is demonstrated in the
correspondence regime.Comment: 23 pages, no figures, submitted for publicatio
Classification of unit-vector fields in convex polyhedra with tangent boundary conditions
A unit-vector field n on a convex three-dimensional polyhedron P is tangent
if, on the faces of P, n is tangent to the faces. A homotopy classification of
tangent unit-vector fields continuous away from the vertices of P is given. The
classification is determined by certain invariants, namely edge orientations
(values of n on the edges of P), kink numbers (relative winding numbers of n
between edges on the faces of P), and wrapping numbers (relative degrees of n
on surfaces separating the vertices of P), which are subject to certain sum
rules. Another invariant, the trapped area, is expressed in terms of these. One
motivation for this study comes from liquid crystal physics; tangent
unit-vector fields describe the orientation of liquid crystals in certain
polyhedral cells.Comment: 21 pages, 2 figure
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