Deflection of Rotating Symmetric Molecules by Inhomogeneous Fields

We consider deflection of rotating symmetric molecules by inhomogeneous optical and static electric fields, compare results with the case of linear molecules, and find new singularities in the distribution of the scattering angle. Scattering of the prolate/oblate molecules is analyzed in detail, and it is shown that the process can be efficiently controlled by means of short and strong femtosecond laser pulses. In particular, the angular dispersion of the deflected molecules may be dramatically reduced by laser-induced molecular pre-alignment. We first study the problem by using a simple classical model, and then find similar results by means of more sophisticated methods, including the formalism of adiabatic invariants and direct numerical simulation of the Euler-Lagrange equations of motion. The suggested control scheme opens new ways for many applications involving molecular focusing, guiding, and trapping by optical and static fields

Parametric derivation of the observable relativistic periastron advance for binary pulsars

We compute the dimensionless relativistic periastron advance parameter $k$, which is measurable from the timing of relativistic binary pulsars. We employ for the computation the recently derived Keplerian-type parametric solution to the post-Newtonian (PN) accurate conservative dynamics of spinning compact binaries moving in eccentric orbits. The parametric solution and hence the parameter $k$ are applicable for the cases of \emph{simple precession}, namely, case (i), the binary consists of equal mass compact objects, having two arbitrary spins, and case (ii), the binary consists of compact objects of arbitrary mass, where only one of them is spinning with an arbitrary spin. Our expression, for the cases considered, is in agreement with a more general formula for the 2PN accurate $k$, relevant for the relativistic double pulsar PSR J0737--3039, derived by Damour and Sch\"afer many years ago, using a different procedure.Comment: 12 pages including 1 figure; submitted to PR

Electric Deflection of Rotating Molecules

We provide a theory of the deflection of polar and non-polar rotating molecules by inhomogeneous static electric field. Rainbow-like features in the angular distribution of the scattered molecules are analyzed in detail. Furthermore, we demonstrate that one may efficiently control the deflection process with the help of short and strong femtosecond laser pulses. In particular the deflection process may by turned-off by a proper excitation, and the angular dispersion of the deflected molecules can be substantially reduced. We study the problem both classically and quantum mechanically, taking into account the effects of strong deflecting field on the molecular rotations. In both treatments we arrive at the same conclusions. The suggested control scheme paves the way for many applications involving molecular focusing, guiding, and trapping by inhomogeneous fields

Vortex-type elastic structured media and dynamic shielding

The paper addresses a novel model of metamaterial structure. A system of spinners has been embedded into a two-dimensional periodic lattice system. The equations of motion of spinners are used to derive the expression for the chiral term in the equations describing the dynamics of the lattice. Dispersion of elastic waves is shown to possess innovative filtering and polarization properties induced by the vortextype nature of the structured media. The related homogenised effective behavior is obtained analytically and it has been implemented to build a shielding cloak around an obstacle. Analytical work is accompanied by numerical illustrations.Comment: 24 pages, 13 figure

Significant g-factor values of a two-electron ground state in quantum dots with spin-orbit coupling

The magnetization of semiconductor quantum dots in the presence of spin-orbit coupling and interactions is investigated numerically. When the dot is occupied by two electrons we find that a level crossing between the two lowest many-body eigenstates may occur as a function of the spin-orbit coupling strength. This level crossing is accompanied by a non-vanishing magnetization of the ground-state. Using first order perturbation theory as well as exact numerical diagonalization of small clusters we show that the tendency of interactions to cause Stoner-like instability is enhanced by the SO coupling. The resulting g-factor can have a significant value, and thus may influence g-factor measurements. Finally we propose an experimental method by which the predicted phenomenon can be observed.Comment: 7+ pages, 7 figure

Contraction of broken symmetries via Kac-Moody formalism

I investigate contractions via Kac-Moody formalism. In particular, I show how the symmetry algebra of the standard 2-D Kepler system, which was identified by Daboul and Slodowy as an infinite-dimensional Kac-Moody loop algebra, and was denoted by ${\mathbb H}_2$, gets reduced by the symmetry breaking term, defined by the Hamiltonian $$H(\beta)= \frac 1 {2m} (p_1^2+p_2^2)- \frac \alpha r - \beta r^{-1/2} \cos ((\phi-\gamma)/2).$$ For this $H (\beta)$ I define two symmetry loop algebras ${\mathfrak L}_{i}(\beta), i=1,2$, by choosing the `basic generators' differently. These ${\mathfrak L}_{i}(\beta)$ can be mapped isomorphically onto subalgebras of ${\mathbb H}_2$, of codimension 2 or 3, revealing the reduction of symmetry. Both factor algebras ${\mathfrak L}_i(\beta)/I_i(E,\beta)$, relative to the corresponding energy-dependent ideals $I_i(E,\beta)$, are isomorphic to ${\mathfrak so}(3)$ and ${\mathfrak so}(2,1)$ for $E0$, respectively, just as for the pure Kepler case. However, they yield two different non-standard contractions as $E \to 0$, namely to the Heisenberg-Weyl algebra ${\mathfrak h}_3={\mathfrak w}_1$ or to an abelian Lie algebra, instead of the Euclidean algebra ${\mathfrak e}(2)$ for the pure Kepler case. The above example suggests a general procedure for defining generalized contractions, and also illustrates the {\em `deformation contraction hysteresis'}, where contraction which involve two contraction parameters can yield different contracted algebras, if the limits are carried out in different order.Comment: 21 pages, 1 figur

Time Evolution of Temperature and Entropy of Various Collapsing Domain Walls

We investigate the time evolution of the temperature and entropy of gravitationally collapsing domain walls as seen by an asymptotic observer. In particular, we seek to understand how topology and the addition of a cosmological constant affect the gravitational collapse. Previous work has shown that the entropy of a spherically symmetric collapsing domain approaches a constant. In this paper, we reproduce these results, using both a fully quantum and a semi-classical approach, then we repeat the process for a de Sitter Schwarzschild domain wall (spherical with cosmological constant) and a (3+1) BTZ domain wall (cylindrical). We do this by coupling a scalar field to the background of the domain wall and analyzing the spectrum of radiation as a function of time. We find that the spectrum is quasi-thermal, with the degree of thermality increasing as the domain wall approaches the horizon. The thermal distribution allows for the determination of the temperature as a function of time, and we find that the late time temperature is very close to the Hawking temperature and that it also exhibits the proper scaling with the mass. From the temperature we find the entropy. Since the collapsing domain wall is what forms a black hole, we can compare the results to those of the standard entropy-area relation. We find that the entropy does in fact approach a constant that is close to the Hawking entropy. However, both the de Sitter Schwarzschild domain wall and the (3+1) BTZ domain wall show periods of decreasing entropy, which suggests that spontaneous collapse may be prevented.Comment: This paper is a merging of two previously submitted papers: Time Evolution of Temperature and Entropy of a Gravitationally Collapsing Cylinder [arXiv:1106.2278]; Time Evolution of Temperature and Entropy of a Gravitationally Collapsing de Sitter Schwarzschild Domain Wal

Galactic Spiral Structure

We describe the structure and composition of six major stellar streams in a population of 20 574 local stars in the New Hipparcos Reduction with known radial velocities. We find that, once fast moving stars are excluded, almost all stars belong to one of these streams. The results of our investigation have lead us to re-examine the hydrogen maps of the Milky Way, from which we identify the possibility of a symmetric two-armed spiral with half the conventionally accepted pitch angle. We describe a model of spiral arm motions which matches the observed velocities and composition of the six major streams, as well as the observed velocities of the Hyades and Praesepe clusters at the extreme of the Hyades stream. We model stellar orbits as perturbed ellipses aligned at a focus in coordinates rotating at the rate of precession of apocentre. Stars join a spiral arm just before apocentre, follow the arm for more than half an orbit, and leave the arm soon after pericentre. Spiral pattern speed equals the mean rate of precession of apocentre. Spiral arms are shown to be stable configurations of stellar orbits, up to the formation of a bar and/or ring. Pitch angle is directly related to the distribution of orbital eccentricities in a given spiral galaxy. We show how spiral galaxies can evolve to form bars and rings. We show that orbits of gas clouds are stable only in bisymmetric spirals. We conclude that spiral galaxies evolve toward grand design two-armed spirals. We infer from the velocity distributions that the Milky Way evolved into this form about 9 Gyrs ago.Comment: Published in Proc Roy Soc A. A high resolution version of this file can be downloaded from http://papers.rqgravity.net/SpiralStructure.pdf. A simplified account with animations begins at http://rqgravity.net/SpiralStructur