Quantum Fokker-Planck Dynamics

The Fokker-Planck equation is a partial differential equation which is a key ingredient in many models in physics. This paper aims to obtain a quantum counterpart of Fokker-Planck dynamics, as a means to describing quantum Fokker-Planck dynamics. Given that relevant models relate to the description of large systems, the quantization of the Fokker-Planck equation should be done in a manner that respects this fact, and is therefore carried out within the setting of non-commutative analysis based on general von Neumann algebras. Within this framework we present a quantization of the generalized Laplace operator, and then go on to incorporate a potential term conditioned to noncommutative analysis. In closing we then construct and examine the asymptotic behaviour of the corresponding Markov semigroups. We also present a noncommutative Csiszar-Kullback inequality formulated in terms of a notion of relative entropy, and show that for more general systems, good behaviour with respect to this notion of entropy ensures similar asymptotic behaviour of the relevant dynamics.Comment: The final version submitted to AHP. A brief account of applied quantization as well as the comprehensive description of closability of quantum Laplacian is adde

Eta and eta' mesons production at COSY-11

The low emittance and small momentum spread of the proton and deuteron beams of the Cooler Synchrotron COSY combined with the high mass resolution of the COSY-11 detection system permit to study the creation of mesons in the nucleon-nucleon interaction down to the fraction of MeV with respect to the kinematical threshold. At such small excess energies, the ejectiles possess low relative momenta and are predominantly produced with the relative angular momentum equal to zero. Taking advantage of these conditions we have performed investigations aiming to determine the mechanism of the production of eta and eta' mesons in the collision of hadrons as well as the hadronic interaction of these mesons with nucleons and nuclei. In this proceedings we address the ongoing studies of the spin and isospin dependence for the production of the eta and eta' mesons in free and quasi-free nucleon-nucleon collisions. New results on the spin observables for the vec(p)p --> pp eta reaction, combined with the previously determined total cross section isospin dependence, reveal a statistically significant indication that the excitation of the nucleon to the S11(1535) resonance, the process which intermediates the production of the eta meson in the nucleon-nucleon interactions, is predominantly due to the exchange of the pi meson between the colliding nucleons.Comment: Invited talk at MESON 2006: 9th International Workshop on Meson Production, Properties and Interactions, Cracow, Poland, 9-13 Jun 200

Near threshold eta meson production in dp collisions

Preliminary results of recent measurements of the near threshold eta meson production in the dp-->dp eta reaction are presented. The experiment was performed at the COSY-Juelich accelerator with the use of the COSY-11 detection system. Data were taken for three values of deuteron beam momenta corresponding to excess energies of 3.2, 6.1 and 9.2 MeV. The energy dependence of the total cross section confirms a strong effect of the final state interaction.Comment: Talk given at 9th International Workshop on Meson Production, Properties and Interaction, Cracow, Poland, 9-13 June 2006. 5 pages, 3 figure

Study of the 3He-eta system in d-p collisions at COSY-11

We present preliminary results from dp --> 3He X (X=pi0,eta) measurements near the eta production threshold. The data were taken during a slow ramping of the COSY internal deuteron beam scattered on a proton target. The 3He ejectiles were registered with the COSY-11 detection setup. The ongoing data analysis should deliver high precision data for the dp --> 3He eta total and differential cross sections for the excess energies in the range from threshold up to 9 MeV. The preliminary excitation function for the reaction dp --> 3He pi0 does not show any structure which could originate from the decay of 3He-eta bound state. We present also a threshold excitation curve for the dp --> 3He X channel. Contrary to corresponding results from SATURNE we see no cusp in the vicinity of the eta threshold.Comment: 8 pages; 5 figures; Talk at Eta05 Workshop on Production and Decay of eta and eta-prime Mesons, Cracow, Poland, 15-18 Sep 2005; Acta Phys. Slovaca, in prin

Study of the production mechanism of the eta meson by means of analysing power measurements

Information about the production mechanism of the eta meson in proton-proton collisions can be inferred by confronting the experimental studies on the analysing power for the p(pol)p --> pp eta reaction with the theoretical predictions of this observable. Results show that the predictions of pure pseudoscalar- or vector meson exchange model are insufficient to describe the analysing powers.Comment: 4 pages, 4 figures, Presented at MESON 2006: 9th International Workshop on Meson Production, Properties and Interactions, Cracow, Poland, 9-13 Jun 200

A method to disentangle single- and multi-meson production in missing mass spectra from quasi-free pn --> pn X reactions

The separation of contributions from multi- and single-meson production in the missing mass spectrum of the quasi-free pn --> pnX reaction constitutes a~challenging task when the reaction is studied close to threshold. This is especially true if the resolution of the mass determination is comparable with the excess energy and if the investigated signal appears close to the kinematical limit. In this article we outline a method which permits the extraction of the signal originating from the creation of a single meson without the necessity of conducting model-dependent simulations. For the pd --> pnXp(spectator) reactions, the method allows one to combine events corresponding to multi-meson production at various excess energies with respect to the pn --> pn meson process, and hence leads to an increase of the statistics needed for the determination of the shape of the multi-meson background. As an example of the application of the method, we demonstrate that the evaluation of the data from the pd --> pnXp(sp) process according to the described technique enables one to extract a signal of the pn --> pn eta reaction whose shape is consistent with expectations, supporting the correctness and usefulness of the method introduced.Comment: 14 pages, 10 figure