Anomalous Transport in Velocity Space, from Fokker-Planck to General Equation

The problem of anomalous diffusion in momentum (velocity) space is considered based on the master equation and the appropriate probability transition function (PTF). The approach recently developed by the author for coordinate space, is applied with necessary modifications to velocity space. A new general equation for the time evolution of the momentum distribution function in momentum space is derived. This allows the solution of various problems of anomalous transport when the probability transition function (PTF) has a long tail in momentum space. For the opposite cases of the PTF rapidly decreasing as a function of transfer momenta (when large transfer momenta are strongly suppressed), the developed approach allows us to consider strongly non-equilibrium cases of the system evolution. The stationary and non-stationary solutions are studied. As an example, the particular case of the Boltzmann-type PT-function for collisions of heavy and light particles with the determined (prescribed) distribution function, which can be strongly non-equilibrium, is considered within the proposed general approach. The appropriate diffusion and friction coefficients are found. The Einstein relation between the friction and diffusion coefficients is shown to be violated in these cases.Comment: 23 pages, 0 figure

Kramers-Kronig Relations For The Dielectric Function And The Static Conductivity Of Coulomb Systems

The mutual influence of singularities of the dielectric permittivity e(q,w) in a Coulomb system in two limiting cases w tends to zero, q tends to zero, and opposite q tends to zero, w tends to zero is established. It is shown that the dielectric permittivity e(q,w) satisfies the Kramers-Kronig relations, which possesses the singularity due to a finite value of the static conductivity. This singularity is associated with the long "tails" of the time correlation functions.Comment: 9 pages, 0 figure

Diffusion in a Time-dependent External Field

The problem of diffusion in a time-dependent (and generally inhomogeneous) external field is considered on the basis of a generalized master equation with two times, introduced in [1,2]. We consider the case of the quasi Fokker-Planck approximation, when the probability transition function for diffusion (PTD-function) does not possess a long tail in coordinate space and can be expanded as a function of instantaneous displacements. The more complicated case of long tails in the PTD will be discussed separately. We also discuss diffusion on the basis of hydrodynamic and kinetic equations and show the validity of the phenomenological approach. A new type of "collision" integral is introduced for the description of diffusion in a system of particles, which can transfer from a moving state to the rest state (with some waiting time distribution). The solution of the appropriate kinetic equation in the external field also confirms the phenomenological approach of the generalized master equation.Comment: 18 pages, no figure

Exploring Pompeii: discovering hospitality through research synergy

Hospitality research continues to broaden through an ever-increasing dialogue and alignment with a greater number of academic disciplines. This paper demonstrates how an enhanced understanding of hospitality can be achieved through synergy between archaeology, the classics and sociology. It focuses on classical Roman life, in particular Pompeii, to illustrate the potential for research synergy and collaboration, to advance the debate on hospitality research and to encourage divergence in research approaches. It demonstrates evidence of commercial hospitality activities through the excavation hotels, bars and taverns, restaurants and fast food sites. The paper also provides an example of the benefits to be gained from multidisciplinary analysis of hospitality and tourism

Tests of model of color reconnection and a search for glueballs using gluon jets with a rapidity gap

Gluon jets with a mean energy of 22 GeV and purity of 95% are selected from hadronic Z0 decay events produced in e+e- annihilations. A subsample of these jets is identified which exhibits a large gap in the rapidity distribution of particles within the jet. After imposing the requirement of a rapidity gap, the gluon jet purity is 86%. These jets are observed to demonstrate a high degree of sensitivity to the presence of color reconnection, i.e. higher order QCD processes affecting the underlying color structure. We use our data to test three QCD models which include a simulation of color reconnection: one in the Ariadne Monte Carlo, one in the Herwig Monte Carlo, and the other by Rathsman in the Pythia Monte Carlo. We find the Rathsman and Ariadne color reconnection models can describe our gluon jet measurements only if very large values are used for the cutoff parameters which serve to terminate the parton showers, and that the description of inclusive Z0 data is significantly degraded in this case. We conclude that color reconnection as implemented by these two models is disfavored. The signal from the Herwig color reconnection model is less clear and we do not obtain a definite conclusion concerning this model. In a separate study, we follow recent theoretical suggestions and search for glueball-like objects in the leading part of the gluon jets. No clear evidence is observed for these objects.Comment: 42 pages, 18 figure

Search for Yukawa Production of a Light Neutral Higgs Boson at LEP

Within a Two-Higgs-Doublet Model (2HDM) a search for a light Higgs boson in the mass range of 4-12 GeV has been performed in the Yukawa process e+e- -> b bbar A/h -> b bbar tau+tau-, using the data collected by the OPAL detector at LEP between 1992 and 1995 in e+e- collisions at about 91 GeV centre-of-mass energy. A likelihood selection is applied to separate background and signal. The number of observed events is in good agreement with the expected background. Within a CP-conserving 2HDM type II model the cross-section for Yukawa production depends on xiAd = |tan beta| and xihd = |sin alpha/cos beta| for the production of the CP-odd A and the CP-even h, respectively, where tan beta is the ratio of the vacuum expectation values of the Higgs doublets and alpha is the mixing angle between the neutral CP-even Higgs bosons. From our data 95% C.L. upper limits are derived for xiAd within the range of 8.5 to 13.6 and for xihd between 8.2 to 13.7, depending on the mass of the Higgs boson, assuming a branching fraction into tau+tau- of 100%. An interpretation of the limits within a 2HDM type II model with Standard Model particle content is given. These results impose constraints on several models that have been proposed to explain the recent BNL measurement of the muon anomalous magnetic moment.Comment: 24 pages, 9 figures, Submitted to Euro. Phys. J.

Search for the Standard Model Higgs Boson with the OPAL Detector at LEP

This paper summarises the search for the Standard Model Higgs boson in e+e- collisions at centre-of-mass energies up to 209 GeV performed by the OPAL Collaboration at LEP. The consistency of the data with the background hypothesis and various Higgs boson mass hypotheses is examined. No indication of a signal is found in the data and a lower bound of 112.7GeV/C^2 is obtained on the mass of the Standard Model Higgs boson at the 95% CL.Comment: 51 pages, 21 figure

Scaling violations of quark and gluon jet fragmentation functions in e+e- annihilations at sqrt(s) = 91.2 and 183-209 GeV

Flavour inclusive, udsc and b fragmentation functions in unbiased jets, and flavour inclusive, udsc, b and gluon fragmentation functions in biased jets are measured in e+e- annihilations from data collected at centre-of-mass energies of 91.2, and 183-209 GeV with the OPAL detector at LEP. The unbiased jets are defined by hemispheres of inclusive hadronic events, while the biased jet measurements are based on three-jet events selected with jet algorithms. Several methods are employed to extract the fragmentation functions over a wide range of scales. Possible biases are studied in the results are obtained. The fragmentation functions are compared to results from lower energy e+e- experiments and with earlier LEP measurements and are found to be consistent. Scaling violations are observed and are found to be stronger for the fragmentation functions of gluon jets than for those of quarks. The measured fragmentation functions are compared to three recent theoretical next-to-leading order calculations and to the predictions of three Monte Carlo event generators. While the Monte Carlo models are in good agreement with the data, the theoretical predictions fail to describe the full set of results, in particular the b and gluon jet measurements.Comment: 46 pages, 17 figures, Submitted to Eur. Phys J.