Sewing sound quantum flesh onto classical bones

Semiclassical transformation theory implies an integral representation for stationary-state wave functions $\psi_m(q)$ in terms of angle-action variables ($\theta,J$). It is a particular solution of Schr\"{o}dinger's time-independent equation when terms of order $\hbar^2$ and higher are omitted, but the pre-exponential factor $A(q,\theta)$ in the integrand of this integral representation does not possess the correct dependence on $q$. The origin of the problem is identified: the standard unitarity condition invoked in semiclassical transformation theory does not fix adequately in $A(q,\theta)$ a factor which is a function of the action $J$ written in terms of $q$ and $\theta$. A prescription for an improved choice of this factor, based on succesfully reproducing the leading behaviour of wave functions in the vicinity of potential minima, is outlined. Exact evaluation of the modified integral representation via the Residue Theorem is possible. It yields wave functions which are not, in general, orthogonal. However, closed-form results obtained after Gram-Schmidt orthogonalization bear a striking resemblance to the exact analytical expressions for the stationary-state wave functions of the various potential models considered (namely, a P\"{o}schl-Teller oscillator and the Morse oscillator).Comment: RevTeX4, 6 page

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

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

Tunable graphene-based polarizer

It is shown that an attenuated total reflection structure containing a graphene layer can operate as a tunable polarizer of the electromagnetic radiation. The polarization angle is controlled by adjusting the voltage applied to graphene via external gate. The mechanism is based on the resonant coupling of $p-$polarized electromagnetic waves to the surface plasmon-polaritons in graphene. The presented calculations show that, at resonance, the reflected wave is almost 100% $s-$polarized.Comment: submitted to the Applied Physics Letter

Kcne4 deletion sex- and age-specifically impairs cardiac repolarization in mice.

Myocardial repolarization capacity varies with sex, age, and pathology; the molecular basis for this variation is incompletely understood. Here, we show that the transcript for KCNE4, a voltage-gated potassium (Kv) channel β subunit associated with human atrial fibrillation, was 8-fold more highly expressed in the male left ventricle compared with females in young adult C57BL/6 mice (P < 0.05). Similarly, Kv current density was 25% greater in ventricular myocytes from young adult males (P < 0.05). Germ-line Kcne4 deletion eliminated the sex-specific Kv current disparity by diminishing ventricular fast transient outward current (Ito,f) and slowly activating K(+) current (IK,slow1). Kcne4 deletion also reduced Kv currents in male mouse atrial myocytes, by >45% (P < 0.001). As we previously found for Kv4.2 (which generates mouse Ito,f), heterologously expressed KCNE4 functionally regulated Kv1.5 (the Kv α subunit that generates IKslow1 in mice). Of note, in postmenopausal female mice, ventricular repolarization was impaired by Kcne4 deletion, and ventricular Kcne4 expression increased to match that of males. Moreover, castration diminished male ventricular Kcne4 expression 2.8-fold, whereas 5α-dihydrotestosterone (DHT) implants in castrated mice increased Kcne4 expression >3-fold (P = 0.01) to match noncastrated levels. KCNE4 is thereby shown to be a DHT-regulated determinant of cardiac excitability and a molecular substrate for sex- and age-dependent cardiac arrhythmogenesis

Proposed Rabi-Kondo Correlated State in a Laser-Driven Semiconductor Quantum Dot

Spin exchange between a single-electron charged quantum dot and itinerant electrons leads to an emergence of Kondo correlations. When the quantum dot is driven resonantly by weak laser light, the resulting emission spectrum allows for a direct probe of these correlations. In the opposite limit of vanishing exchange interaction and strong laser drive, the quantum dot exhibits coherent oscillations between the single-spin and optically excited states. Here, we show that the interplay between strong exchange and non-perturbative laser coupling leads to the formation of a new nonequilibrium quantum-correlated state, characterized by the emergence of a laser-induced secondary spin screening cloud, and examine the implications for the emission spectrum

Abelian Gauge Theory in de Sitter Space

Quantization of spinor and vector free fields in 4-dimensional de Sitter space-time, in the ambient space notation, has been studied in the previous works. Various two-points functions for the above fields are presented in this paper. The interaction between the spinor field and the vector field is then studied by the abelian gauge theory. The U(1) gauge invariant spinor field equation is obtained in a coordinate independent way notation and their corresponding conserved currents are computed. The solution of the field equation is obtained by use of the perturbation method in terms of the Green's function. The null curvature limit is discussed in the final stage.Comment: 10 pages, typos corrected, reference adde