Generalized Euler Angle Paramterization for SU(N)

In a previous paper (math-ph/0202002) an Euler angle parameterization for SU(4) was given. Here we present the derivation of a generalized Euler angle parameterization for SU(N). The formula for the calculation of the Haar measure for SU(N) as well as its relation to Marinov's volume formula for SU(N) will also be derived. As an example of this parameterization's usefulness, the density matrix parameterization and invariant volume element for a qubit/qutrit, three qubit and two three-state systems, also known as two qutrit systems, will also be given.Comment: 36 pages, no figures; added qubit/qutrit work, corrected minor definition problems and clarified Haar measure derivation. To be published in J. Phys. A: Math. and Ge

A Parametrization of Bipartite Systems Based on SU(4) Euler Angles

In this paper we give an explicit parametrization for all two qubit density matrices. This is important for calculations involving entanglement and many other types of quantum information processing. To accomplish this we present a generalized Euler angle parametrization for SU(4) and all possible two qubit density matrices. The important group-theoretical properties of such a description are then manifest. We thus obtain the correct Haar (Hurwitz) measure and volume element for SU(4) which follows from this parametrization. In addition, we study the role of this parametrization in the Peres-Horodecki criteria for separability and its corresponding usefulness in calculating entangled two qubit states as represented through the parametrization.Comment: 23 pages, no figures; changed title and abstract and rewrote certain areas in line with referee comments. To be published in J. Phys. A: Math. and Ge

Semi-classical buckling of stiff polymers

A quantitative theory of the buckling of a worm like chain based on a semi-classical approximation of the partition function is presented. The contribution of thermal fluctuations to the force-extension relation that allows to go beyond the classical Euler buckling is derived in the linear and non-linear regime as well. It is shown that the thermal fluctuations in the nonlinear buckling regime increase the end-to-end distance of the semiflexible rod if it is confined to 2 dimensions as opposed to the 3 dimensional case. Our approach allows a complete physical understanding of buckling in D=2 and in D=3 below and above the Euler transition.Comment: Revtex, 17 pages, 4 figure

Neutron induced background in the COMPTEL detector on the Gamma Ray Observatory

Interactions of neutrons in a prototype of the Compton imaging telescope (COMPTEL) gamma ray detector for the Gamma Ray Observatory were studied to determine COMPTEL's sensitivity as a neutron telescope and to estimate the gamma ray background resulting from neutron interactions. The IUCF provided a pulsed neutron beam at five different energies between 18 and 120 MeV. These measurements showed that the gamma ray background from neutron interactions is greater than previously expected. It was thought that most such events would be due to interactions in the upper detector modules of COMPTEL and could be distinguished by pulse shape discrimination. Rather, the bulk of the gamma ray background appears to be due to interactions in passive material, primarily aluminum, surrounding the D1 modules. In a considerable fraction of these interactions, two or more gamma rays are produced simultaneously, with one interacting in the D1 module and the other interacting in the module of the lower (D2) detector. If the neutron interacts near the D1 module, the D1 D2 time of flight cannot distinguish such an event from a true gamma ray event. In order to assess the significance of this background, the flux of neutrons in orbit has been estimated based on observed events with neutron pulse shape signature in D1. The strength of this neutron induced background is estimated. This is compared with the rate expected from the isotropic cosmic gamma ray flux

Peculiar Features of the Velocity Field of OB Associations and the Spiral Structure of the Galaxy

Some of the peculiar features of the periodic velocity-field structure for OB associations can be explained by using the model of Roberts and Hausman (1984), in which the behavior of a system of dense clouds is considered in a perturbed potential. The absence of statistically significant variations in the azimuthal velocity across the Carina arm, probably, results from its sharp increase behind the shock front, which is easily blurred by distance errors. The existence of a shock wave in the spiral arms and, at the same time, the virtually free motion of OB associations in epicycles can be reconciled in the model of particle clouds with a mean free path of 0.2-2 kpc. The velocity field of OB associations exhibits two appreciable nonrandom deviations from an ideal spiral pattern: a 0.5-kpc displacement of the Cygnus- and Carina-arm fragments from one another and a weakening of the Perseus arm in quadrant III. However, the identified fragments of the Carina, Cygnus, and Perseus arms do not belong to any of the known types of spurs.Comment: 14 pages, 3 postscript figures, to be published in Astronomy Letter

Quasi-doubly periodic solutions to a generalized Lame equation

We consider the algebraic form of a generalized Lame equation with five free parameters. By introducing a generalization of Jacobi's elliptic functions we transform this equation to a 1-dim time-independent Schroedinger equation with (quasi-doubly) periodic potential. We show that only for a finite set of integral values for the five parameters quasi-doubly periodic eigenfunctions expressible in terms of generalized Jacobi functions exist. For this purpose we also establish a relation to the generalized Ince equation.Comment: 15 pages,1 table, accepted for publication in Journal of Physics

The Influence of Bars on Nuclear Activity

We test ideas on fueling of galactic nuclei by bar-driven inflow by comparing the detection rate and intensity of nuclear H II regions and AGNs among barred and unbarred galaxies in a sample of over 300 spirals selected from our recent optical spectroscopic survey of nearby galaxies. Among late-type spirals (Sc-Sm), but not early-type (S0/a-Sbc), we observe in the barred group a very marginal increase in the detection rate of H II nuclei and a corresponding decrease in the incidence of AGNs. The minor differences in the detection rates, however, are statistically insignificant, most likely stemming from selection effects and not from a genuine influence from the bar. The presence of a bar seems to have no noticeable impact on the likelihood of a galaxy to host either nuclear star formation or an AGN. The nuclei of early-type barred spirals do exhibit measurably higher star-formation rates than their unbarred counterparts, as indicated by either the luminosity or the equivalent width of H-alpha emission. By contrast, late-type spirals do not show such an effect. Bars have a negligible effect on the strength of the AGNs in our sample, regardless of the Hubble type of the host galaxy. This result confirms similar conclusions reached by other studies based on much smaller samples.Comment: To appear in the Astrophysical Journal. LaTex, 31 pages including 6 postscript figures and 3 tables. AAStex macros include

Uniform semiclassical trace formula for U(3) --> SO(3) symmetry breaking

We develop a uniform semiclassical trace formula for the density of states of a three-dimensional isotropic harmonic oscillator (HO), perturbed by a term $\propto r^4$. This term breaks the U(3) symmetry of the HO, resulting in a spherical system with SO(3) symmetry. We first treat the anharmonic term in semiclassical perturbation theory by integration of the action of the perturbed periodic HO orbits over the manifold $\mathbb{C}$P$^2$ which characterizes their 4-fold degeneracy. Then we obtain an analytical uniform trace formula which in the limit of strong perturbations (or high energy) asymptotically goes over into the correct trace formula of the full anharmonic system with SO(3) symmetry, and in the limit $\epsilon$ (or energy) $\to 0$ restores the HO trace formula with U(3) symmetry. We demonstrate that the gross-shell structure of this anharmonically perturbed system is dominated by the two-fold degenerate diameter and circular orbits, and {\it not} by the orbits with the largest classical degeneracy, which are the three-fold degenerate tori with rational ratios $\omega_r:\omega_\phi=N:M$ of radial and angular frequencies. The same holds also for the limit of a purely quartic spherical potential $V(r)\propto r^4$.Comment: LaTeX (revtex4), 26pp., 5 figures, 1 table; final version to be published in J. Phys. A (without appendices C and D

Hilbert--Schmidt volume of the set of mixed quantum states

We compute the volume of the convex N^2-1 dimensional set M_N of density matrices of size N with respect to the Hilbert-Schmidt measure. The hyper--area of the boundary of this set is also found and its ratio to the volume provides an information about the complex structure of M_N. Similar investigations are also performed for the smaller set of all real density matrices. As an intermediate step we analyze volumes of the unitary and orthogonal groups and of the flag manifolds.Comment: 13 revtex pages, ver 3: minor improvement

Topological Phases near a Triple Degeneracy

We study the pattern of three state topological phases that appear in systems with real Hamiltonians and wave functions. We give a simple geometric construction for representing these phases. We then apply our results to understand previous work on three state phases. We point out that the ``mirror symmetry'' of wave functions noticed in microwave experiments can be simply understood in our framework.Comment: 4 pages, 1 figure, to appear in Phys. Rev. Let