Relativistic N-Boson Systems Bound by Oscillator Pair Potentials

We study the lowest energy E of a relativistic system of N identical bosons bound by harmonic-oscillator pair potentials in three spatial dimensions. In natural units the system has the semirelativistic ``spinless-Salpeter'' Hamiltonian H = \sum_{i=1}^N \sqrt{m^2 + p_i^2} + \sum_{j>i=1}^N gamma |r_i - r_j|^2, gamma > 0. We derive the following energy bounds: E(N) = min_{r>0} [N (m^2 + 2 (N-1) P^2 / (N r^2))^1/2 + N (N-1) gamma r^2 / 2], N \ge 2, where P=1.376 yields a lower bound and P=3/2 yields an upper bound for all N \ge 2. A sharper lower bound is given by the function P = P(mu), where mu = m(N/(gamma(N-1)^2))^(1/3), which makes the formula for E(2) exact: with this choice of P, the bounds coincide for all N \ge 2 in the Schroedinger limit m --> infinity.Comment: v2: A scale analysis of P is now included; this leads to revised energy bounds, which coalesce in the large-m limi

Discrete spectra of semirelativistic Hamiltonians from envelope theory

We analyze the (discrete) spectrum of the semirelativistic ``spinless-Salpeter'' Hamiltonian H = \beta \sqrt{m^2 + p^2} + V(r), beta > 0, where V(r) represents an attractive, spherically symmetric potential in three dimensions. In order to locate the eigenvalues of H, we extend the ``envelope theory,'' originally formulated only for nonrelativistic Schroedinger operators, to the case of Hamiltonians H involving the relativistic kinetic-energy operator. If V(r) is a convex transformation of the Coulomb potential -1/r and a concave transformation of the harmonic-oscillator potential r^2, both upper and lower bounds on the discrete eigenvalues of H can be constructed, which may all be expressed in the form E = min_{r>0} [ \beta \sqrt{m^2 + P^2/r^2} + V(r) ] for suitable values of the numbers P here provided. At the critical point, the relative growth to the Coulomb potential h(r) = -1/r must be bounded by dV/dh < 2 \beta/\pi.Comment: 20 pages, 2 tables, 4 figure

Energy bounds for the spinless Salpeter equation: harmonic oscillator

We study the eigenvalues E_{n\ell} of the Salpeter Hamiltonian H = \beta\sqrt(m^2 + p^2) + vr^2, v>0, \beta > 0, in three dimensions. By using geometrical arguments we show that, for suitable values of P, here provided, the simple semi-classical formula E = min_{r > 0} {v(P/r)^2 + \beta\sqrt(m^2 + r^2)} provides both upper and lower energy bounds for all the eigenvalues of the problem.Comment: 8 pages, 1 figur

Energy bounds for the spinless Salpeter equation

We study the spectrum of the spinless-Salpeter Hamiltonian H = \beta \sqrt{m^2 + p^2} + V(r), where V(r) is an attractive central potential in three dimensions. If V(r) is a convex transformation of the Coulomb potential -1/r and a concave transformation of the harmonic-oscillator potential r^2, then upper and lower bounds on the discrete eigenvalues of H can be constructed, which may all be expressed in the form E = min_{r>0} [ \beta \sqrt{m^2 + P^2/r^2} + V(r) ] for suitable values of P here provided. At the critical point the relative growth to the Coulomb potential h(r)=-1/r must be bounded by dV/dh < 2\beta/\pi.Comment: 11 pages, 1 figur

A comparison of ultraviolet sensitivities in universal, nonuniversal, and split extra dimensional models

We discuss the origin of ultraviolet sensitivity in extra dimensional theories, and compare and contrast the cutoff dependences in universal, nonuniversal and split five dimensional models. While the gauge bosons and scalars are in the five dimensional bulk in all scenarios, the locations of the fermions are different in different cases. In the universal model all fermions can travel in the bulk, in the nonuniversal case they are all confined at the brane, while in the split scenario some are in the bulk and some are in the brane. A possible cure from such divergences is also discussed.Comment: 9 pages, Latex, no figure, v2: further clarifications and references added, accepted for publication in Phys. Rev.

Remarks on flavour mixings from orbifold compactification

We consider 5d SU(5) GUT models based on the orbifold $S^1/(Z_2 \times Z_2')$, and study the different possibilities of placing the SU(5) matter multiplets in three possible locations, namely, the two branes at the two orbifold fixed points and SU(5) bulk. We demonstrate that if flavour hierarchies originate solely from geometrical suppressions due to wavefunction normalisation of fields propagating in the bulk, then it is not possible to satisfy even the gross qualitative behaviour of the CKM and MNS matrices regardless of where we place the matter multiplets.Comment: 4 pages, Late

Extended analytical study of the free-wing/free-trimmer concept

The free wing/free trimmer concept was analytically studied in order to: (1) compare the fore and aft trimmer configurations on the basis of equal lift capability, rather than equal area; (2) assess the influence of tip mounted aft trimmers, both free and fixed, on the lateral directional modes and turbulence responses; (3) examine the feasibility of using differential tip mounted trimmer deflection for lateral control; (4) determine the effects of independent fuselage attitude on the lateral directional behavior; and (5) estimate the influence of wing sweep on dynamic behavior and structural weight. Results indicate that the forward trimmer concept is feasible with the reduced size examined, but it remains inferior to the aft trimmer in every respect except structural weight. Differential motion of the aft trimmer is found to provide powerful lateral control; while the effect of fuselage deck angle is a reduction of the dutch roll damping ratio for nose-down attitudes

Spiked oscillators: exact solution

A procedure to obtain the eigenenergies and eigenfunctions of a quantum spiked oscillator is presented. The originality of the method lies in an adequate use of asymptotic expansions of Wronskians of algebraic solutions of the Schroedinger equation. The procedure is applied to three familiar examples of spiked oscillators

Limits of the energy-momentum tensor in general relativity

A limiting diagram for the Segre classification of the energy-momentum tensor is obtained and discussed in connection with a Penrose specialization diagram for the Segre types. A generalization of the coordinate-free approach to limits of Paiva et al. to include non-vacuum space-times is made. Geroch's work on limits of space-times is also extended. The same argument also justifies part of the procedure for classification of a given spacetime using Cartan scalars.Comment: LaTeX, 21 page

Thermal dissipation in quantum turbulence

The microscopic mechanism of thermal dissipation in quantum turbulence has been numerically studied by solving the coupled system involving the Gross-Pitaevskii equation and the Bogoliubov-de Gennes equation. At low temperatures, the obtained dissipation does not work at scales greater than the vortex core size. However, as the temperature increases, dissipation works at large scales and it affects the vortex dynamics. We successfully obtained the mutual friction coefficients of the vortex dynamics as functions of temperature, which can be applied to the vortex dynamics in dilute Bose-Einstein condensates.Comment: 4 pages, 6 figures, submitted to AP