Some realizable joint measurements of complementary observables

Noncommuting quantum observables, if considered asunsharp observables, are simultaneously measurable. This fact is exemplified for complementary observables in two-dimensional state spaces. Two proposals of experimentally feasible joint measurements are presented for pairs of photon or neutron polarization observables and for path and interference observables in a photon split-beam experiment. A recent experiment proposed and performed by Mittelstaedt, Prieur, and Schieder in Cologne is interpreted as a partial version of the latter example.Work partly supported by the DFG, Bonn, and the BMFT, Bonn.Dedicated to Professor Ulrich Hauser on the occasion of his 60th birthday, November 1986.     

Quantum localization observables and accelerated frames

We define quantum observables associated with Einstein localization in space-time. These observables are built on Poincaré and dilatation generators. Their commutators are given by spin observables defined from the same symmetry generators. Their shifts under transformations to uniformly accelerated frames are evaluated through algebraic computations in conformal algebra. Spin number is found to vary under such transformations with a variation involving further observables introduced as irreducible quadrupole momenta. Quadrupole observables may be dealt with as non commutative polarizations which allow one to define step operators increasing or decreasing the spin number by unity. Received: 11 December 1997 / Revised: 1st July 1998 / Accepted: 1st September 1998     

Investigations of quark fragmentation universality

We propose event cuts in deep inelastic scattering, suitable for an examination of quark fragmentation universality. We compare the current hemisphere of the Breit frame with the hemispheres in annihilation events, using Monte Carlo simulations. The agreement between the two processes is improved after the suggested event cuts are introduced. A method to study the scale evolution in the quark hemispheres using data from fixed-energy experiments is presented. This makes it possible to use the high statistics from LEP1 also at scales below the mass. We also discuss observables which are sensitive to the dynamics of regions closer to the remnant. The observables probe the relatively clean region on the current side of the hardest emission in the event, and can be used to distinguish between different assumptions about remnant effects and mechanisms for the parton evolution. Received: 3 November 1998 / Revised version: 25 January 1999 / Published online: 30 June 1999     

Regge approach to charged pion photoproduction at invariant energies above 2 GeV

A Regge model with absorptive corrections is employed in a global analysis of the world data on positive and negative pion photoproduction for photon energies from 3 to 8GeV. In this region resonance contributions are expected to be negligible so that the available experimental information on differential cross-sections and single polarization observables at - t ⩽ 2 GeV^2 allows us to determine the non-resonant part of the reaction amplitude reliably. The model amplitude is then used to predict observables for photon energies below 3GeV. Differences between our predictions and data in this energy region are systematically examined as possible signals for the presence of excited baryons. We find that the data available for the polarized photon asymmetry show promising resonance signatures at invariant energies around 2GeV. With regard to differential cross-sections the analysis of negative pion photoproduction data, obtained recently at JLab, indicates likewise the presence of resonance structures around 2GeV.     

Unsharp particle-wave duality in a photon split-beam experiment

In a quantum mechanical two-slit experiment one can observe a single photon simultaneously as particle (measuring the path) and as wave (measuring the interference pattern) if the path and the interference pattern are measured in the sense of unsharp observables. These theoretical predictions are confirmed experimentally by a photon split-beam experiment using a modified Mach—Zehnder interferometer.     

Final state photon production at LEP

We present a detailed study of photon production in hadronic events in electron-positron annihilation at LEP energies. We show that estimates of the inclusive photon spectrum using the quark-to-photon fragmentation function determined using the ALEPH ‘photon’ + 1 jet data agree well with the observations of the OPAL collaboration. This agreement shows that the photon fragmentation function determined in this way can be used for inclusive observables. We also compare next-to-leading order and beyond leading logarithm predictions obtained using the numerically resummed solutions of the fragmentation function evolution equation of Bourhis, Fontannaz and Guillet and Glück, Reya and Vogt with the data. Moreover, in order to check the general behaviour of the fragmentation function, we consider an analytic series expansion in the strong coupling. We find that the parameterizations are inaccurate at large x values. While the OPAL data is in broad agreement with estimates based on any of these approaches, the ALEPH data prefers the resummed BFG parameterization. Finally, there is some ambiguity as to whether the fragmentation function is treated as or . We show that at present this ambiguity affects mainly the prediction for the ‘photon’ + 1 jet rate at large z. Received: 9 June 1998 / Published online: 21 August 1998     

Reducing backaction when measuring temporal correlations in quantum systems

Dynamic correlations of quantum observables are challenging to measure due to measurement backaction incurred at early times. Recent work [P. Uhrich et al., Phys. Rev. A 96, 022127 (2017)] has shown that ancilla-based noninvasive measurements are able to reduce this backaction, allowing for dynamic correlations of single-site spin observables to be measured. We generalise this result to correlations of arbitrary spin observables and extend the measurement protocol to simultaneous noninvasive measurements which allow for real and imaginary parts of correlations to be extracted from a single set of measurements. We use positive operator-valued measures to analyse the dynamics generated by the ancilla-based measurements. Using this framework we prove that special observables exist for which measurement backaction is of no concern, so that dynamic correlations of these can be obtained without making use of ancillas.     

Dilepton creation based on an analytic hydrodynamic solution

High-energy collisions of various nuclei, so called “Little Bangs” are observed in various experiments of heavy ion colliders. The time evolution of the strongly interacting quark-gluon plasma created in heavy ion collisions can be described by hydrodynamical models. After expansion and cooling, the hadrons are created in a freeze-out. Their distribution describes the final state of this medium. To investigate the time evolution one needs to analyze penetrating probes, such as direct photon or dilepton observables, as these particles are created throughout the evolution of the medium. In this paper we analyze an 1+3 dimensional analytic solution of relativistic hydrodynamics, and we calculate dilepton transverse momentum and invariant mass distributions. We investigate the dependence of dilepton production on time evolution parameters, such as emission duration and equation of state. Using parameters from earlier fits of this model to photon and hadron spectra, we compare our calculations to measurements as well. The most important feature of this work is that dilepton observables are calculated from an exact, analytic, 1+3D solution of relativistic hydrodynamics that is also compatible with hadronic and direct photon observables.     

Equivalent Theories and Changing Hamiltonian Observables in General Relativity

Change and local spatial variation are missing in Hamiltonian general relativity according to the most common definition of observables as having 0 Poisson bracket with all first-class constraints. But other definitions of observables have been proposed. In pursuit of Hamiltonian–Lagrangian equivalence, Pons, Salisbury and Sundermeyer use the Anderson–Bergmann–Castellani gauge generator G, a tuned sum of first-class constraints. Kucha? waived the 0 Poisson bracket condition for the Hamiltonian constraint to achieve changing observables. A systematic combination of the two reforms might use the gauge generator but permit non-zero Lie derivative Poisson brackets for the external gauge symmetry of General Relativity. Fortunately one can test definitions of observables by calculation using two formulations of a theory, one without gauge freedom and one with gauge freedom. The formulations, being empirically equivalent, must have equivalent observables. For de Broglie-Proca non-gauge massive electromagnetism, all constraints are second-class, so everything is observable. Demanding equivalent observables from gauge Stueckelberg–Utiyama electromagnetism, one finds that the usual definition fails while the Pons–Salisbury–Sundermeyer definition with G succeeds. This definition does not readily yield change in GR, however. Should GR’s external gauge freedom of general relativity share with internal gauge symmetries the 0 Poisson bracket (invariance), or is covariance (a transformation rule) sufficient? A graviton mass breaks the gauge symmetry (general covariance), but it can be restored by parametrization with clock fields. By requiring equivalent observables, one can test whether observables should have 0 or the Lie derivative as the Poisson bracket with the gauge generator G. The latter definition is vindicated by calculation. While this conclusion has been reported previously, here the calculation is given in some detail.     

Nodal Sets for Groundstates of Schrödinger Operators with Zero Magnetic Field in Non Simply Connected Domains

We investigate nodal sets of magnetic Schr?dinger operators with zero magnetic field, acting on a non simply connected domain in ℝ². For the case of circulation 1/2 of the magnetic vector potential around each hole in the region, we obtain a characterisation of the nodal set, and use this to obtain bounds on the multiplicity of the groundstate. For the case of one hole and a fixed electric potential, we show that the first eigenvalue takes its highest value for circulation 1/2. Received: 23 July 1998 / Accepted: 17 November 1998     

Measurement of αs with radiative hadronic events

Hadronic final states with a hard isolated photon are studied using data taken at centre-of-mass energies around the mass of the Z boson with the OPAL detector at LEP. The strong coupling α_s is extracted by comparing data and QCD predictions for event shape observables at average reduced centre-of-mass energies ranging from 24 GeV to 78 GeV, and the energy dependence of α_s is studied. Our results are consistent with the running of α_s as predicted by QCD and show that within the uncertainties of our analysis event shapes in hadronic Z decays with hard and isolated photon radiation can be described by QCD at reduced centre-of-mass energies. Combining all values from different event shape observables and energies gives α_s(M_Z)=0.1182±0.0015(stat.)±0.0101(syst.).     

Estimation of shift parameters of a quantum state

Estimation of shift parameters such as arrival time, phase, angle of rotation, position of a non-relativistic or relativistic particle is considered. An approach from the point of view of quantum estimation theory enables to give a proper definition of the time observable and the position observables of a massless relativistic particle, i.e. observables to which there do not correspond self-adjoint operators. Some new inequalities for estimates of shift parameters are obtained; in particular a rigorous uncertainty relation for coordinates of the photon is established.     

Critical dynamics in clusters of noble gas atoms

The multi-fragmentation dynamics of noble gas atomic clusters is considered for different statistically distributed deposited energies. The conditions giving rise to the development of criticality in the cluster evolution are revealed from an analysis of the signals in the fragment mass distribution. The time dependence of the observables related to critical exponents is studied. It is demonstrated that in a certain regime the cluster exhibits a behavior which can be identified as the precursor of a second-order liquid-gas phase transition. Received 1st September 1998 and Received in final form 14 January 1999     

On direct photon production in Pb+Pb and Au+Au collisions

We attempt in this paper to deal with some aspects of the direct photon production phenomenon mainly in the Pb+Pb and Au+Au collisions on the basis of a model for production of the same particle species in PP collisions. The results have, thereafter, been converted to those for a few AB/AA interactions through an appropriate mechanism. Comparison of the theoretical results obtained on the basis of model-based calculations with measured data on the relevant observables leads to a fair agreement between them. This reflects modestly the fair achievements attained by the models that are made use of in the present work.     

Determination of the 3Pj Phase Shifts from Nucleon-Nucleon Data: A Critical Evaluation and a Surprising Result

 It is shown that the neutron-proton (proton-proton) phase shifts cannot be determined to less than % (%) uncertainty at low energies ( MeV), even if high-accuracy nucleon-nucleon data were to become available for currently inaccessible observables. For a more accurate determination, appropriate theoretical constraints have to be invoked, but their accuracy can be judged only from the comparison of rigorous three-nucleon continuum calculations with particular three-nucleon observables. Received February 17, 1998; revised July 2, 1998; accepted for publication December 16, 1998     

Propagation of Correlations in Quantum Lattice Systems

We provide a simple proof of the Lieb-Robinson bound and use it to prove the existence of the dynamics for interactions with polynomial decay. We then use our results to demonstrate that there is an upper bound on the rate at which correlations between observables with separated support can accumulate as a consequence of the dynamics.     

Statistische Bewegungsgesetze relaxierender Systeme

Dynamical properties of a physical systemσ in the vicinity of a stable stationary stateZ can be determined approximately from observation of this state, that is from the correlation functions of one or several observables in the stateZ. This will be done with utilization of the principle of unprejudized estimate. The number of observables and the degree of correlation functions observed, define a certain “degree of observation” of the system. Approximations of the dynamics of the system belonging to several degrees of observations are compared and discussed in detail. The general formalism is demonstrated by a simple example.     

Twist-3 single-spin asymmetries in semi-inclusive deep-inelastic scattering

The single-spin asymmetries for a longitudinally polarized lepton beam or a longitudinally polarized nucleon target in semi-inclusive deep-inelastic scattering are twist-3 observables. We study these asymmetries in a simple diquark spectator model of the nucleon. Analogous to the case of transverse target polarization, non-vanishing asymmetries are generated by gluon exchange between the struck quark and the target system. It is pointed out that the coupling of the virtual photon to the diquark is needed in order to preserve electromagnetic gauge invariance at the twist-3 level. The calculation indicates that previous analyses of these observables are incomplete.     

Pion-Exchange Effects in Elastic Backward Proton-Deuteron Scattering

 The elastic backward proton-deuteron scattering is analyzed within a covariant approach based on the deuteron vertex function obtained by the Bethe-Salpeter equation with realistic meson-exchange interaction. Contributions of the one-nucleon and one-pion exchange mechanisms to the cross section and polarization observables are investigated in explicit form. Results of numerical calculations for the cross section, tensor analyzing power and spin transfers are presented. The one-pion exchange contribution is essential for describing the spin-averaged cross section, while in polarization observables it is found to have a small effect. Received December 22, 1998; revised November 8, 1999; accepted November 10, 1999