Fundamental length in quantum theories with PT-symmetric Hamiltonians

The direct observability of coordinates x is often lost in PT-symmetric quantum theories. A manifestly non-local Hilbert-space metric $\Theta$ enters the double-integral normalization of wave functions $\psi(x)$ there. In the context of scattering, the (necessary) return to the asymptotically fully local metric has been shown feasible, for certain family of PT-symmetric toy Hamiltonians H at least, in paper I (M. Znojil, Phys. Rev. D 78 (2008) 025026). Now we show that in a confined-motion dynamical regime the same toy model proves also suitable for an explicit control of the measure or width $\theta$ of its non-locality. For this purpose each H is assigned here, constructively, the complete menu of its hermitizing metrics $\Theta=\Theta_\theta$ distinguished by their optional "fundamental lengths" $\theta\in (0,\infty)$. The local metric of paper I recurs at $\theta=0$ while the most popular CPT-symmetric hermitization proves long-ranged, with $\theta=\infty$.Comment: 31 pp, 3 figure

Gegenbauer-solvable quantum chain model

In an innovative inverse-problem construction the measured, experimental energies $E_1$, $E_2$, ...$E_N$ of a quantum bound-state system are assumed fitted by an N-plet of zeros of a classical orthogonal polynomial $f_N(E)$. We reconstruct the underlying Hamiltonian $H$ (in the most elementary nearest-neighbor-interaction form) and the underlying Hilbert space ${\cal H}$ of states (the rich menu of non-equivalent inner products is offered). The Gegenbauer's ultraspherical polynomials $f_n(x)=C_n^\alpha(x)$ are chosen for the detailed illustration of technicalities.Comment: 29 pp., 1 fi

A New Template Family For The Detection Of Gravitational Waves From Comparable Mass Black Hole Binaries

In order to improve the phasing of the comparable-mass waveform as we approach the last stable orbit for a system, various re-summation methods have been used to improve the standard post-Newtonian waveforms. In this work we present a new family of templates for the detection of gravitational waves from the inspiral of two comparable-mass black hole binaries. These new adiabatic templates are based on re-expressing the derivative of the binding energy and the gravitational wave flux functions in terms of shifted Chebyshev polynomials. The Chebyshev polynomials are a useful tool in numerical methods as they display the fastest convergence of any of the orthogonal polynomials. In this case they are also particularly useful as they eliminate one of the features that plagues the post-Newtonian expansion. The Chebyshev binding energy now has information at all post-Newtonian orders, compared to the post-Newtonian templates which only have information at full integer orders. In this work, we compare both the post-Newtonian and Chebyshev templates against a fiducially exact waveform. This waveform is constructed from a hybrid method of using the test-mass results combined with the mass dependent parts of the post-Newtonian expansions for the binding energy and flux functions. Our results show that the Chebyshev templates achieve extremely high fitting factors at all PN orders and provide excellent parameter extraction. We also show that this new template family has a faster Cauchy convergence, gives a better prediction of the position of the Last Stable Orbit and in general recovers higher Signal-to-Noise ratios than the post-Newtonian templates.Comment: Final published version. Accepted for publication in Phys. Rev.

Sphinx measurements of the 2009 solar minimum x-ray emission

The SphinX X-ray spectrophotometer on the CORONAS-PHOTON spacecraft measured soft X-ray emission in the 1-15 keV energy range during the deep solar minimum of 2009 with a sensitivity much greater than GOES. Several intervals are identified when the X-ray flux was exceptionally low, and the flux and solar X-ray luminosity are estimated. Spectral fits to the emission at these times give temperatures of 1.7-1.9 MK and emission measures between 4 x 10^47 cm^-3 and 1.1 x 10^48 cm^-3. Comparing SphinX emission with that from the Hinode X-ray Telescope, we deduce that most of the emission is from general coronal structures rather than confined features like bright points. For one of 27 intervals of exceptionally low activity identified in the SphinX data, the Sun's X-ray luminosity in an energy range roughly extrapolated to that of ROSAT (0.1-2.4 keV) was less than most nearby K and M dwarfs.Comment: Astrophysical Journal, in press. 14 pp, 3 figure

Coronal loop hydrodynamics. The solar flare observedon November 12 1980 revisited: the UV line emission

We revisit a well-studied solar flare whose X-ray emission originating from a simple loop structure was observed by most of the instruments on board SMM on November 12 1980. The X-ray emission of this flare, as observed with the XRP, was successfully modeled previously. Here we include a detailed modeling of the transition region and we compare the hydrodynamic results with the UVSP observations in two EUV lines, measured in areas smaller than the XRP rasters, covering only some portions of the flaring loop (the top and the foot-points). The single loop hydrodynamic model, which fits well the evolution of coronal lines (those observed with the XRP and the \FeXXI 1354.1 \AA line observed with the UVSP) fails to model the flux level and evolution of the \OV 1371.3 \AA line.Comment: A&A, in press, 6 pages, 5 figure

Weak dipole moment of τ\tau in e+e−e^+e^- collisions with longitudinally polarized electrons

It is pointed out that certain CP-odd momentum correlations in the production and subsequent decay of tau pairs in $e^+e^-$ collisions get enhanced when the $e^-$ is longitudinally polarized. Analytic expressions for these correlations are obtained for the single-pion decay mode of $\tau$ when $\tau^+\tau^-$ have a ``weak" dipole form factor (WDFF) coupling to $Z$ . For $e^+e^-$ collisions at the $Z$ peak, a sensitivity of about 1-5$\times 10^{-17}$\mbox{$e$ cm} for the $\tau$ WDFF can be reached using a {\em single} $\tau^+\tau^-$ decay channel, with $10^6\, Z$'s likely to be available at the SLC at Stanford with $e^-$ polarization of 62\%-75\%.Comment: 9 pages, Latex, PRL-TH-93/17 (Revised

Measurement of the τ\tau electric dipole moment using longitudinal polarization of e+e−e^+e^- beams

Certain CP-odd momentum correlations in the production and subsequent decay of $\tau$ pairs in $e^+ e^-$ collisions are enhanced significantly when the $e^+$ and $e^-$ beams are longitudinally polarized. These may be used to probe the real and imaginary parts of $d_\tau^\gamma$, the electric dipole moment of the $\tau$. Closed-form expressions for these ``vector correlations'' and the standard deviation of the operators defining them due to standard model interactions are presented for the two-body final states of $\tau$ decays. If 42\% average polarization of each beam is achieved, as proposed for the tau-charm factories, with equal integrated luminosities for each sign of polarization and a total yield of $2\cdot 10^7$ $\tau^+ \tau^-$ pairs, it is possible to attain sensitivities for $\vert\delta {\rm Re} d_{\tau}^{\gamma}\vert$ of $8\cdot 10^{-19}$, $1\cdot 10^{-19}$, $1\cdot 10^{-19}$ $e$ cm respectively and for $\vert\delta {\rm Im} d_{\tau}^{\gamma}\vert$ of $4\cdot 10^{-14}$, $6\cdot 10^{-15}$, $5\cdot 10^{-16}$ $e$ cm respectively at the three operating center-of-mass energies of 3.67, 4.25 and 10.58 GeV. These bounds emerge when the effects of a posible weak dipole form factor $d_\tau^Z$ are negligible as is the case when it is of the same order of magnitude as $d_\tau^\gamma$. Furthermore, in such a polarization experiment where different polarizations are possible, a model-independent disentangling of their individual effects is possible, and a technique to achieve this is described. A strong longitudinal polarization physics programme at the tau-charm factory appears warranted.Comment: 30 pages, latex, no figure

Self-Consistent MHD Modeling of a Coronal Mass Ejection, Coronal Dimming, and a Giant Cusp-Shaped Arcade Formation

We performed magnetohydrodynamic simulation of coronal mass ejections (CMEs) and associated giant arcade formations, and the results suggested new interpretations of observations of CMEs. We performed two cases of the simulation: with and without heat conduction. Comparing between the results of the two cases, we found that reconnection rate in the conductive case is a little higher than that in the adiabatic case and the temperature of the loop top is consistent with the theoretical value predicted by the Yokoyama-Shibata scaling law. The dynamical properties such as velocity and magnetic fields are similar in the two cases, whereas thermal properties such as temperature and density are very different.In both cases, slow shocks associated with magnetic reconnectionpropagate from the reconnection region along the magnetic field lines around the flux rope, and the shock fronts form spiral patterns. Just outside the slow shocks, the plasma density decreased a great deal. The soft X-ray images synthesized from the numerical results are compared with the soft X-ray images of a giant arcade observed with the Soft X-ray Telescope aboard {\it Yohkoh}, it is confirmed that the effect of heat conduction is significant for the detailed comparison between simulation and observation. The comparison between synthesized and observed soft X-ray images provides new interpretations of various features associated with CMEs and giant arcades.Comment: 39 pages, 18 figures. Accepted for publication in the Astrophysical Journal. The PDF file with high resplution figures can be downloaded from http://www.kwasan.kyoto-u.ac.jp/~shiota/study/ApJ62426.preprint.pdf

Director configuration of planar solitons in nematic liquid crystals

The director configuration of disclination lines in nematic liquid crystals in the presence of an external magnetic field is evaluated. Our method is a combination of a polynomial expansion for the director and of further analytical approximations which are tested against a numerical shooting method. The results are particularly simple when the elastic constants are equal, but we discuss the general case of elastic anisotropy. The director field is continuous everywhere apart from a straight line segment whose length depends on the value of the magnetic field. This indicates the possibility of an elongated defect core for disclination lines in nematics due to an external magnetic field.Comment: 12 pages, Revtex, 8 postscript figure

Stochastic Analysis of Dimerization Systems

The process of dimerization, in which two monomers bind to each other and form a dimer, is common in nature. This process can be modeled using rate equations, from which the average copy numbers of the reacting monomers and of the product dimers can then be obtained. However, the rate equations apply only when these copy numbers are large. In the limit of small copy numbers the system becomes dominated by fluctuations, which are not accounted for by the rate equations. In this limit one must use stochastic methods such as direct integration of the master equation or Monte Carlo simulations. These methods are computationally intensive and rarely succumb to analytical solutions. Here we use the recently introduced moment equations which provide a highly simplified stochastic treatment of the dimerization process. Using this approach, we obtain an analytical solution for the copy numbers and reaction rates both under steady state conditions and in the time-dependent case. We analyze three different dimerization processes: dimerization without dissociation, dimerization with dissociation and hetero-dimer formation. To validate the results we compare them with the results obtained from the master equation in the stochastic limit and with those obtained from the rate equations in the deterministic limit. Potential applications of the results in different physical contexts are discussed.Comment: 10 figure