A Geometrical Method of Decoupling

The computation of tunes and matched beam distributions are essential steps in the analysis of circular accelerators. If certain symmetries - like midplane symmetrie - are present, then it is possible to treat the betatron motion in the horizontal, the vertical plane and (under certain circumstances) the longitudinal motion separately using the well-known Courant-Snyder theory, or to apply transformations that have been described previously as for instance the method of Teng and Edwards. In a preceeding paper it has been shown that this method requires a modification for the treatment of isochronous cyclotrons with non-negligible space charge forces. Unfortunately the modification was numerically not as stable as desired and it was still unclear, if the extension would work for all thinkable cases. Hence a systematic derivation of a more general treatment seemed advisable. In a second paper the author suggested the use of real Dirac matrices as basic tools to coupled linear optics and gave a straightforward recipe to decouple positive definite Hamiltonians with imaginary eigenvalues. In this article this method is generalized and simplified in order to formulate a straightforward method to decouple Hamiltonian matrices with eigenvalues on the real and the imaginary axis. It is shown that this algebraic decoupling is closely related to a geometric "decoupling" by the orthogonalization of the vectors $\vec E$, $\vec B$ and $\vec P$, that were introduced with the so-called "electromechanical equivalence". We present a structure-preserving block-diagonalization of symplectic or Hamiltonian matrices, respectively. When used iteratively, the decoupling algorithm can also be applied to n-dimensional systems and requires ${\cal O}(n^2)$ iterations to converge to a given precision.Comment: 13 pages, 1 figur

Analysis of OPM potentials for multiplet states of 3d transition metal atoms

We apply the optimized effective potential method (OPM) to the multiplet energies of the 3d$^n$ transition metal atoms, where the orbital dependence of the energy functional with respect to orbital wave function is the single-configuration HF form. We find that the calculated OPM exchange potential can be represented by the following two forms. Firstly, the difference between OPM exchange potentials of the multiplet states can be approximated by the linear combination of the potentials derived from the Slater integrals $F^2({\rm 3d,3d})$ and $F^4({\rm 3d,3d})$ for the average energy of the configuration. Secondly, the OPM exchange potential can be expressed as the linear combination of the OPM exchange potentials of the single determinants.Comment: 15 pages, 6 figures, to be published in J. Phys.

Wigner's DD-matrix elements for SU(3)SU(3) - A Generating Function Approach

A generating function for the Wigner's $D$-matrix elements of $SU(3)$ is derived. From this an explicit expression for the individual matrix elements is obtained in a closed form.Comment: RevTex 3.0, 22 pages, no figure

Variational perturbation approach to the Coulomb electron gas

The efficiency of the variational perturbation theory [Phys. Rev. C {\bf 62}, 045503 (2000)] formulated recently for many-particle systems is examined by calculating the ground state correlation energy of the 3D electron gas with the Coulomb interaction. The perturbation beyond a variational result can be carried out systematically by the modified Wick's theorem which defines a contraction rule about the renormalized perturbation. Utilizing the theorem, variational ring diagrams of the electron gas are summed up. As a result, the correlation energy is found to be much closer to the result of the Green's function Monte Carlo calculation than that of the conventional ring approximation is.Comment: 4 pages, 3 figure

Gupta-Bleuler quantization for minimally coupled scalar fields in de Sitter space

We present in this paper a fully covariant quantization of the minimally-coupled massless field on de Sitter space. We thus obtain a formalism free of any infrared (e.g logarithmic) divergence. Our method is based on a rigorous group theoretical approach combined with a suitable adaptation (Krein spaces) of the Wightman-G\"{a}rding axiomatic for massless fields (Gupta-Bleuler scheme). We make explicit the correspondence between unitary irreducible representations of the de Sitter group and the field theory on de Sitter space-time. The minimally-coupled massless field is associated with a representation which is the lowest term of the discrete series of unitary representations of the de Sitter group. In spite of the presence of negative norm modes in the theory, no negative energy can be measured: expressions as \le n_{k_1}n_{k_2}...|T_{00}|n_{k_1}n_{k_2}...\re are always positive.Comment: 20 pages, appear in class. quantum gra

Two-Bit Gates are Universal for Quantum Computation

A proof is given, which relies on the commutator algebra of the unitary Lie groups, that quantum gates operating on just two bits at a time are sufficient to construct a general quantum circuit. The best previous result had shown the universality of three-bit gates, by analogy to the universality of the Toffoli three-bit gate of classical reversible computing. Two-bit quantum gates may be implemented by magnetic resonance operations applied to a pair of electronic or nuclear spins. A ``gearbox quantum computer'' proposed here, based on the principles of atomic force microscopy, would permit the operation of such two-bit gates in a physical system with very long phase breaking (i.e., quantum phase coherence) times. Simpler versions of the gearbox computer could be used to do experiments on Einstein-Podolsky-Rosen states and related entangled quantum states.Comment: 21 pages, REVTeX 3.0, two .ps figures available from author upon reques

Measuring the Polarization of a Rapidly Precessing Deuteron Beam

This paper describes a time-marking system that enables a measurement of the in-plane (horizontal) polarization of a 0.97-GeV/c deuteron beam circulating in the Cooler Synchrotron (COSY) at the Forschungszentrum J\"ulich. The clock time of each polarimeter event is used to unfold the 120-kHz spin precession and assign events to bins according to the direction of the horizontal polarization. After accumulation for one or more seconds, the down-up scattering asymmetry can be calculated for each direction and matched to a sinusoidal function whose magnitude is proportional to the horizontal polarization. This requires prior knowledge of the spin tune or polarization precession rate. An initial estimate is refined by re-sorting the events as the spin tune is adjusted across a narrow range and searching for the maximum polarization magnitude. The result is biased toward polarization values that are too large, in part because of statistical fluctuations but also because sinusoidal fits to even random data will produce sizeable magnitudes when the phase is left free to vary. An analysis procedure is described that matches the time dependence of the horizontal polarization to templates based on emittance-driven polarization loss while correcting for the positive bias. This information will be used to study ways to extend the horizontal polarization lifetime by correcting spin tune spread using ring sextupole fields and thereby to support the feasibility of searching for an intrinsic electric dipole moment using polarized beams in a storage ring. This paper is a combined effort of the Storage Ring EDM Collaboration and the JEDI Collaboration.Comment: 28 pages, 15 figures, prepared for Physical Review ST - Accelerators and Beam

Separation of the Exchange-Correlation Potential into Exchange plus Correlation: an Optimized Effective Potential Approach

Most approximate exchange-correlation functionals used within density functional theory are constructed as the sum of two distinct contributions for exchange and correlation. Separating the exchange component from the entire functional is useful since, for exchange, exact relations exist under uniform density scaling and spin scaling. In the past, accurate exchange-correlation potentials have been generated from essentially exact densities constructed using information from either quantum chemistry or quantum Monte Carlo calculations but they have not been correctly decomposed into their separate exchange and correlation components, except for two-electron systems. exchange and correlation components (except for two-electron systems). Using a recently proposed method, equivalent to the solution of an optimized effective potential problem with the corresponding orbitals replaced by the exact Kohn-Sham orbitals, we obtain the separation according to the density functional theory definition. We compare the results for the Ne and Be atoms with those obtained by the previously used approximate separation scheme

Proteomic analysis of Plasmodium in the mosquito: progress and pitfalls

Here we discuss proteomic analyses of whole cell preparations of the mosquito stages of malaria parasite development (i.e. gametocytes, microgamete, ookinete, oocyst and sporozoite) of Plasmodium berghei. We also include critiques of the proteomes of two cell fractions from the purified ookinete, namely the micronemes and cell surface. Whereas we summarise key biological interpretations of the data, we also try to identify key methodological constraints we have met, only some of which we were able to resolve. Recognising the need to translate the potential of current genome sequencing into functional understanding, we report our efforts to develop more powerful combinations of methods for the in silico prediction of protein function and location. We have applied this analysis to the proteome of the male gamete, a cell whose very simple structural organisation facilitated interpretation of data. Some of the in silico predictions made have now been supported by ongoing protein tagging and genetic knockout studies. We hope this discussion may assist future studie