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