Geometry of entangled states, Bloch spheres and Hopf fibrations

We discuss a generalization to 2 qubits of the standard Bloch sphere representation for a single qubit, in the framework of Hopf fibrations of high dimensional spheres by lower dimensional spheres. The single qubit Hilbert space is the 3-dimensional sphere S3. The S2 base space of a suitably oriented S3 Hopf fibration is nothing but the Bloch sphere, while the circular fibres represent the qubit overall phase degree of freedom. For the two qubits case, the Hilbert space is a 7-dimensional sphere S7, which also allows for a Hopf fibration, with S3 fibres and a S4 base. A main striking result is that suitably oriented S7 Hopf fibrations are entanglement sensitive. The relation with the standard Schmidt decomposition is also discussedComment: submitted to J. Phys.

A Precision Measurement of pp Elastic Scattering Cross Sections at Intermediate Energies

We have measured differential cross sections for \pp elastic scattering with internal fiber targets in the recirculating beam of the proton synchrotron COSY. Measurements were made continuously during acceleration for projectile kinetic energies between 0.23 and 2.59 GeV in the angular range $30 \leq \theta_{c.m.} \leq 90$ deg. Details of the apparatus and the data analysis are given and the resulting excitation functions and angular distributions presented. The precision of each data point is typically better than 4%, and a relative normalization uncertainty of only 2.5% within an excitation function has been reached. The impact on phase shift analysis as well as upper bounds on possible resonant contributions in lower partial waves are discussed.Comment: 23 pages 29 figure

Measurement of Spin Correlation Parameters ANN_{NN}, ASS_{SS}, and A_SL{SL} at 2.1 GeV in Proton-Proton Elastic Scattering

At the Cooler Synchrotron COSY/J\"ulich spin correlation parameters in elastic proton-proton (pp) scattering have been measured with a 2.11 GeV polarized proton beam and a polarized hydrogen atomic beam target. We report results for A$_{NN}$, A$_{SS}$, and A_${SL}$ for c.m. scattering angles between 30$^o$ and 90$^o$. Our data on A$_{SS}$ -- the first measurement of this observable above 800 MeV -- clearly disagrees with predictions of available of pp scattering phase shift solutions while A$_{NN}$ and A_${SL}$ are reproduced reasonably well. We show that in the direct reconstruction of the scattering amplitudes from the body of available pp elastic scattering data at 2.1 GeV the number of possible solutions is considerably reduced.Comment: 4 pages, 4 figure

Cation- and vacancy-ordering in Li_xCoO_2

Using a combination of first-principles total energies, a cluster expansion technique, and Monte Carlo simulations, we have studied the Li/Co ordering in LiCoO_2 and Li-vacancy/Co ordering in CoO_2. We find: (i) A ground state search of the space of substitutional cation configurations yields the (layered) CuPt structure as the lowest-energy state in the octahedral system LiCoO_2 (and CoO_2), in agreement with the experimentally observed phase. (ii) Finite temperature calculations predict that the solid-state order- disorder transitions for LiCoO_2 and CoO_2 occur at temperatures (~5100 K and ~4400 K, respectively) much higher than melting, thus making these transitions experimentally inaccessible. (iii) The energy of the reaction E(LiCoO_2) - E(CoO_2) - E(Li) gives the average battery voltage V of a Li_xCoO_2/Li cell. Searching the space of configurations for large average voltages, we find that CuPt (a monolayer superlattice) has a high voltage (V=3.78 V), but that this could be increased by cation randomization (V=3.99 V), partial disordering (V=3.86 V), or by forming a 2-layer Li_2Co_2O_4 superlattice along (V=4.90 V).Comment: 12 Pages, RevTeX galley format, 5 figures embedded using epsf Phys. Rev. B (in press, 1998

High resolution study of the Lambda p final state interaction in the reaction p + p -> K+ + (Lambda p)

The reaction pp -> K+ + (Lambda p) was measured at Tp=1.953 GeV and Theta = 0 deg with a high missing mass resolution in order to study the Lambda p final state interaction. The large final state enhancement near the Lambda p threshold can be described using the standard Jost-function approach. The singlet and triplet scattering lengths and effective ranges are deduced by fitting simultaneously the Lambda p invariant mass spectrum and the total cross section data of the free Lambda p scattering.Comment: submitted to Physics Letters B, 10 pages, 3 figure

Upper limits for a narrow resonance in the reaction p + p -> K^+ + (Lambda p)

The reaction pp -> K^+ + (Lambda p) has been measured at T_p = 1.953 GeV and \Theta = 0 deg with a high missing mass resolution in order to study the Lambda p final state interaction. Narrow S = -1 resonances predicted by bag model calculations are not visible in the missing mass spectrum. Small structures observed in a previous experiment are not confirmed. Upper limits for the production cross section of a narrow resonance are deduced for missing masses between 2058 and 2105 MeV/c^2.Comment: 8 pages, 5 figure

Meson Production in p+d Reactions

The production of neutral and charged pions as well as eta mesons is studied in the Delta and N* resonance region, respectively. Heavy A=3 recoils were measured with the GEM detector. The differential cross sections covering the full angular range are compared with model calculations.Comment: 4 pages, latex, 4 figures, talk presented at the XVIIth European Conference on Few-Body Problems in Physics, Evora, Portugal, September 2000; to be published in Nucl. Phys.

Measurement of p + d -> 3He + eta in S(11) Resonance

We have measured the reaction p + d -> 3He + eta at a proton beam energy of 980 MeV, which is 88.5 MeV above threshold using the new ``germanium wall'' detector system. A missing--mass resolution of the detector system of 2.6% was achieved. The angular distribution of the meson is forward peaked. We found a total cross section of (573 +- 83(stat.) +- 69(syst.))nb. The excitation function for the present reaction is described by a Breit Wigner form with parameters from photoproduction.Comment: 8 pages, 2 figures, corrected typos in heade