Relative CC"-Numerical Ranges for Applications in Quantum Control and Quantum Information

Motivated by applications in quantum information and quantum control, a new type of $C$"-numerical range, the relative $C$"-numerical range denoted $W_K(C,A)$, is introduced. It arises upon replacing the unitary group U(N) in the definition of the classical $C$"-numerical range by any of its compact and connected subgroups $K \subset U(N)$. The geometric properties of the relative $C$"-numerical range are analysed in detail. Counterexamples prove its geometry is more intricate than in the classical case: e.g. $W_K(C,A)$ is neither star-shaped nor simply-connected. Yet, a well-known result on the rotational symmetry of the classical $C$"-numerical range extends to $W_K(C,A)$, as shown by a new approach based on Lie theory. Furthermore, we concentrate on the subgroup $SU_{\rm loc}(2^n) := SU(2)\otimes ... \otimes SU(2)$, i.e. the $n$-fold tensor product of SU(2), which is of particular interest in applications. In this case, sufficient conditions are derived for $W_{K}(C,A)$ being a circular disc centered at origin of the complex plane. Finally, the previous results are illustrated in detail for $SU(2) \otimes SU(2)$.Comment: accompanying paper to math-ph/070103

Single \pi^- production in np collisions for excess energies up to 90 MeV

The quasifree reaction np\to pp\pim was studied in a kinematically complete experiment by bombarding a liquid hydrogen target with a deuteron beam of momentum 1.85 GeV/c and analyzing the data along the lines of the spectator model. In addition to the three charged ejectiles the spectator proton was also detected in the large-acceptance time-of-flight spectrometer COSY-TOF. It was identified by its momentum and flight direction thus yielding access to the Fermi motion of the bound neutron and to the effective neutron 4-momentum vector $\mathbb{P}_n$ which differed from event to event. A range of almost 90 MeV excess energy above threshold was covered. Energy dependent angular distributions, invariant mass spectra as well as fully covered Dalitz plots were deduced. Sizeable $pp$ FSI effects were found as were contributions of $p$ and $d$ partial waves. The behavior of the elementary cross section $\sigma_{01}$ close to threshold is discussed in view of new cross section data. In comparison with existing literature data the results provide a sensitive test of the spectator model.Comment: 21 pages, 9 figures, 4 tables, submitted to EPJ

Signatures of Spin and Charge Energy Scales in the Local Moment and Specific Heat of the Two-Dimensional Hubbard Model

Local moment formation driven by the on--site repulsion $U$ is one of the most fundamental features in the Hubbard model. At the simplest level, the temperature dependence of the local moment is expected to have a single structure at $T \sim U$, reflecting the suppression of the double occupancy. In this paper we show new low temperature Quantum Monte Carlo data which emphasize that the local moment also has a signature at a lower energy scale which previously had been thought to characterize only the temperatures below which moments on {\it different} sites begin to correlate locally. We discuss implications of these results for the structure of the specific heat, and connections to quasiparticle resonance and pseudogap formation in the density of states.Comment: 13 pages, 19 figure

Single-Pion Production in pp Collisions at 0.95 GeV/c (II)

The single-pion production reactions $pp\to d\pi^+$, $pp\to np\pi^+$ and $pp\to pp\pi^0$ were measured at a beam momentum of 0.95 GeV/c ($T_p \approx$ 400 MeV) using the short version of the COSY-TOF spectrometer. The central calorimeter provided particle identification, energy determination and neutron detection in addition to time-of-flight and angle measurements from other detector parts. Thus all pion production channels were recorded with 1-4 overconstraints. Main emphasis is put on the presentation and discussion of the $np\pi^+$ channel, since the results on the other channels have already been published previously. The total and differential cross sections obtained are compared to theoretical calculations. In contrast to the $pp\pi^0$ channel we find in the $np\pi^+$ channel a strong influence of the $\Delta$ excitation already at this energy close to threshold. In particular we find a $(3 cos^2\Theta + 1)$ dependence in the pion angular distribution, typical for a pure s-channel $\Delta$ excitation and identical to that observed in the $d\pi^+$ channel. Since the latter is understood by a s-channel resonance in the $^1D_2$ $pn$ partial wave, we discuss an analogous scenario for the $pn\pi^+$ channel

Comparison of Isoscalar Vector Meson Production Cross Sections in Proton-Proton Collisions

The reaction $pp\to pp\bf \omega$ was investigated with the TOF spectrometer, which is an external experiment at the accelerator COSY (Forschungszentrum J\"ulich, Germany). Total as well as differential cross sections were determined at an excess energy of $93 MeV$ ($p_{beam}=2950 MeV/c$). Using the total cross section of $(9.0\pm 0.7 \pm1.1) \mu b$ for the reaction $pp\to pp\omega$ determined here and existing data for the reaction $pp\to pp\bf \phi$, the ratio $\mathcal{R}_{\phi/\omega}=\sigma_\phi/\sigma_\omega$ turns out to be significantly larger than expected by the Okubo-Zweig-Iizuka (OZI) rule. The uncertainty of this ratio is considerably smaller than in previous determinations. The differential distributions show that the $\omega$ production is still dominated by S-wave production at this excess energy, however higher partial waves clearly contribute. A comparison of the measured angular distributions for $\omega$ production to published distributions for $\phi$ production at $83 MeV$ shows that the data are consistent with an identical production mechanism for both vector mesons

Production of ω\omega mesons in proton-proton collisions

The cross section for the production of $\omega$ mesons in proton-proton collisions has been measured in a previously unexplored region of incident energies. Cross sections were extracted at 92 MeV and 173 MeV excess energy, respectively. The angular distribution of the $\omega$ at $\epsilon$=173 MeV is strongly anisotropic, demonstrating the importance of partial waves beyond pure s-wave production at this energy.Comment: 12 pages, 4 figures submitted to Physics Letters B v2: figure 1 added, discussion detailing the data analysis, figure 3 (fig. 2 in v1) modified in line styles and systematic errors displayed on dat

On the SigmaN cusp in the pp -> pK+Lambda reaction

Measurements of the $pp \to pK^+\Lambda$ reaction at $T_p$ = 2.28 GeV have been carried out at COSY-TOF. In addition to the $\Lambda p$ FSI and $N^*$ resonance excitation effects a pronounced narrow structure is observed in the Dalitz plot and in its projection on the $p\Lambda$-invariant mass. The structure appears at the $pp \to$N$K^+\Sigma$ threshold and is interpreted as $\Sigma$N cusp effect. The observed width of 20 MeV/$c^2$ is substantially broader than anticipated from previous inclusive measurements. Angular distributions of this cusp structure are shown to be dissimilar to those in the residual $pK^+\Lambda$ channel, but similar to those observed in the $pK^+\Sigma^0$ channel

On the Production of π+π+\pi^+\pi^+ Pairs in pp Collisions at 0.8 GeV

Data accumulated recently for the exclusive measurement of the $pp\to pp\pi^+\pi^-$ reaction at a beam energy of 0.793 GeV using the COSY-TOF spectrometer have been analyzed with respect to possible events from the $pp \to nn\pi^+\pi^+$ reaction channel. The latter is expected to be the only $\pi\pi$ production channel, which contains no major contributions from resonance excitation close to threshold and hence should be a good testing ground for chiral dynamics in the $\pi\pi$ production process. No single event has been found, which meets all conditions for being a candidate for the $pp \to nn \pi^+\pi^+$ reaction. This gives an upper limit for the cross section of 0.16 $\mu$b (90% C.L.), which is more than an order of magnitude smaller than the cross sections of the other two-pion production channels at the same incident energy

Improved study of a possible Theta+ production in the pp -> p K0 sigma+ reaction with the COSY-TOF spectrometer

The pp -> p K0 Sigma+ reaction was investigated with the TOF spectrometer at COSY at 3.059 GeV/c incident beam momentum. The main objective was to clarify whether or not a narrow exotic S = +1 resnance, the Theta+ pentaquark, is populated at 1.53 GeV/c2 in the K0 p subsystem with a data sample of much higher statistical significance compared to the previously reported data in this channel. An analysis of these data does not confirm the existence of the Theta+ pentaquark. This is expressed as an upper limit for the cross section sigma (pp -> p K0 Sigma+) < 0.15 microbarn at the 95 percent confidence level.Comment: 11 pages, 5 figure