Effects and importance of penetration and growth of lift on space vehicle response

Wind induced aerodynamic response of Saturn C-5 launch vehicle without fin

Spin-2 Amplitudes in Black-Hole Evaporation

Quantum amplitudes for $s=2$ gravitational-wave perturbations of Einstein/scalar collapse to a black hole are treated by analogy with $s=1$ Maxwell perturbations. The spin-2 perturbations split into parts with odd and even parity. We use the Regge-Wheeler gauge; at a certain point we make a gauge transformation to an asymptotically-flat gauge, such that the metric perturbations have the expected falloff behaviour at large radii. By analogy with $s=1$, for $s=2$ natural 'coordinate' variables are given by the magnetic part $H_{ij} (i,j=1,2,3)$ of the Weyl tensor, which can be taken as boundary data on a final space-like hypersurface $\Sigma_F$. For simplicity, we take the data on the initial surface $\Sigma_I$ to be exactly spherically-symmetric. The (large) Lorentzian proper-time interval between $\Sigma_I$ and $\Sigma_F$, measured at spatial infinity, is denoted by $T$. We follow Feynman's $+i\epsilon$ prescription and rotate $T$ into the complex: $T\to{\mid}T{\mid} \exp(-i\theta)$, for $0<\theta\leq\pi/2$. The corresponding complexified {\it classical} boundary-value problem is expected to be well-posed. The Lorentzian quantum amplitude is recovered by taking the limit as $\theta\to 0_+$. For boundary data well below the Planck scale, and for a locally supersymmetric theory, this involves only the semi-classical amplitude $\exp(iS^{(2)}_{\rm class}$, where $S^{(2)}_{\rm class}$ denotes the second-variation classical action. The relations between the $s=1$ and $s=2$ natural boundary data, involving supersymmetry, are investigated using 2-component spinor language in terms of the Maxwell field strength $\phi_{AB}=\phi_{(AB)}$ and the Weyl spinor $\Psi_{ABCD}=\Psi_{(ABCD)}$

Note on restoring manifest rotational symmetry in hyperfine and fine structure in light-front QED

We study the part of the renormalized, cutoff QED light-front Hamiltonian that does not change particle number. The Hamiltonian contains interactions that must be treated in second-order bound state perturbation theory to obtain hyperfine structure. We show that a simple unitary transformation leads directly to the familiar Breit-Fermi spin-spin and tensor interactions, which can be treated in degenerate first-order bound-state perturbation theory, thus simplifying analytic light-front QED calculations. To the order in momenta we need to consider, this transformation is equivalent to a Melosh rotation. We also study how the similarity transformation affects spin-orbit interactions.Comment: 17 pages, latex fil

Asymptotic Freedom and Bound States in Hamiltonian Dynamics

We study a model of asymptotically free theories with bound states using the similarity renormalization group for hamiltonians. We find that the renormalized effective hamiltonians can be approximated in a large range of widths by introducing similarity factors and the running coupling constant. This approximation loses accuracy for the small widths on the order of the bound state energy and it is improved by using the expansion in powers of the running coupling constant. The coupling constant for small widths is order 1. The small width effective hamiltonian is projected on a small subset of the effective basis states. The resulting small matrix is diagonalized and the exact bound state energy is obtained with accuracy of the order of 10% using the first three terms in the expansion. We briefly describe options for improving the accuracy.Comment: plain latex file, 15 pages, 6 latex figures 1 page each, 1 tabl

Relic Radiation from an Evaporating Black Hole

We present a non-string-theoretic calculation of the microcanonical entropy of relic integer-spin Hawking radiation -- at fixed total energy $E$. The only conserved macroscopic quantity is the total energy $E$ (the total energy of the relic radiation). Data for a boundary-value approach, with massless, integer-spin perturbations, are set on initial and final space-like hypersurfaces. In the resulting 1-dimensional statistical-mechanics problem, the real part of the (complex) time separation at spatial infinity, $T = {\mid}T{\mid}\exp(-i\delta), \delta >0$, is the variable conjugate to the total energy. We count the number of weak-field configurations on the final space-like hypersurface with energy $E$. One recovers the Cardy formula and the Bekenstein-Hawking entropy, if Re(T) is of the order of the black-hole life- time, leading to a statistical interpretation of black-hole entropy. The microcanonical entropy includes a logarithmic correction to the black-hole area law, which is {\it universal} (independent of black-hole parameters). Here, the discreteness of the energy levels is crucial. This approach is compared with that of string theory for the transition to the fundamental-string r\'egime in the final stages of evaporation. The squared coupling, $g^2$, regulating the transition to a highly-excited string state and {\it vice versa}, can be related to the angle, $\delta$, of complex-time rotation above. The strong-coupling r\'egime corresponds to a Euclidean black hole, while the physical limit of a Lorentzian space-time (as $\delta \to 0_+$) corresponds to the weak-coupling r\'egime. This resembles the transition to a highly-excited string-like state which subsequently decays into massless particles, thereby avoiding the naked singularity.Comment: To appear in International Journal of Modern Physics

Nonperturbative renormalization in a scalar model within Light-Front Dynamics

Within the covariant formulation of Light-Front Dynamics, in a scalar model with the interaction Hamiltonian $H=-g\psi^{2}(x)\phi(x)$, we calculate nonperturbatively the renormalized state vector of a scalar "nucleon" in a truncated Fock space containing the $N$, $N\pi$ and $N\pi\pi$ sectors. The model gives a simple example of non-perturbative renormalization which is carried out numerically. Though the mass renormalization $\delta m^2$ diverges logarithmically with the cutoff $L$, the Fock components of the "physical" nucleon are stable when $L\to\infty$.Comment: 22 pages, 5 figure

Study of resonance light scattering for remote optical probing

Enhanced scattering and fluorescence processes in the visible and UV were investigated which will enable improved remote measurements of gas properties. The theoretical relationship between scattering and fluorescence from an isolated molecule in the approach to resonance is examined through analysis of the time dependence of re-emitted light following excitation of pulsed incident light. Quantitative estimates are developed for the relative and absolute intensities of fluorescence and resonance scattering. New results are obtained for depolarization of scattering excited by light at wavelengths within a dissociative continuum. The experimental work was performed in two separate facilities. One of these utilizes argon and krypton lasers, single moded by a tilted etalon, and a 3/4 meter double monochromator. This facility was used to determine properties of the re-emission from NO2, I2 and O3 excited by visible light. The second facility involves a narrow-line dye laser, and a 3/4 meter single monochromator. The dye laser produces pulsed light with 5 nsec pulse duration and 0.005 nm spectral width

Black hole evaporation in a spherically symmetric non-commutative space-time

Recent work in the literature has studied the quantum-mechanical decay of a Schwarzschild-like black hole, formed by gravitational collapse, into almost-flat space-time and weak radiation at a very late time. The relevant quantum amplitudes have been evaluated for bosonic and fermionic fields, showing that no information is lost in collapse to a black hole. On the other hand, recent developments in noncommutative geometry have shown that, in general relativity, the effects of non-commutativity can be taken into account by keeping the standard form of the Einstein tensor on the left-hand side of the field equations and introducing a modified energy-momentum tensor as a source on the right-hand side. Relying on the recently obtained non-commutativity effect on a static, spherically symmetric metric, we have considered from a new perspective the quantum amplitudes in black hole evaporation. The general relativity analysis of spin-2 amplitudes has been shown to be modified by a multiplicative factor F depending on a constant non-commutativity parameter and on the upper limit R of the radial coordinate. Limiting forms of F have been derived which are compatible with the adiabatic approximation.Comment: 8 pages, Latex file with IOP macros, prepared for the QFEXT07 Conference, Leipzig, September 200

Ground State Structure and Low Temperature Behaviour of an Integrable Chain with Alternating Spins

In this paper we continue the investigation of an anisotropic integrable spin chain, consisting of spins $s=1$ and $s=\frac{1}{2}$, started in our paper \cite{meissner}. The thermodynamic Bethe ansatz is analysed especially for the case, when the signs of the two couplings $\bar{c}$ and $\tilde{c}$ differ. For the conformally invariant model ($\bar{c}=\tilde{c}$) we have calculated heat capacity and magnetic susceptibility at low temperature. In the isotropic limit our analysis is carried out further and susceptibilities are calculated near phase transition lines (at $T=0$).Comment: 22 pages, LaTeX, uses ioplppt.sty and PicTeX macro