Anomalous Diffusion in Velocity Space

The problem of anomalous diffusion in the momentum space is considered on the basis of the appropriate probability transition function (PTF). New general equation for description of the diffusion of heavy particles in the gas of the light particles is formulated on basis of the new approach similar to one in coordinate space (S. Trigger et al.). The obtained results permit to describe the various situations when the probability transition function (PTF) has a long tail in the momentum space. The effective friction and diffusion coefficients are found.Comment: 11 pages, no figures and table

Velocity-Dependent Friction and Diffusion for Grains in Neutral Gases, Dusty Plasmas and Active Systems

A self-consistent and universal description of friction and diffusion for Brownian particles (grains) in different systems, as a gas with Boltzmann collisions, dusty plasma with ion absorption by grains, and for active particles (e.g., cells in biological systems) is suggested on the basis of the appropriate Fokker-Planck equation. Restrictions for application of the Fokker-Planck equation to the problem of velocity-dependent friction and diffusion coefficients are found. General description for this coefficient is formulated on the basis of master equation. Relation of the diffusion coefficient in the coordinate and velocity spaces is found for active (capable to transfer momentum to the ambient media) and passive particles in the framework of the Fokker-Planck equation. The problem of anomalous space diffusion is formulated on the basis of the appropriate probability transition (PT) function. The method of partial differentiation is avoided to construct the correct probability distributions for arbitrary distances, what is important for applications to different stochastic problems. Generale equation for time-dependent PT function is formulated and discussed. Generalized friction in the velocity space is determined and applied to describe the friction force itself as well as the drag force in the case of a non-zero driven ion velocity in plasmas. The negative friction due to ion scattering on grains exists and can be realized for the appropriate experimental conditions.Comment: 21 page

Constraining CP-Violating TGCs and Measuring W-Polarization at OPAL

A measurement of the polarization of W bosons in semi-leptonically decaying W pairs produced at 189 GeV is presented. Rates of longitudinally and transversely polarized W bosons and correlation between two W bosons are studied. The spin properties of the leptonically decaying W boson in the W pairs was used to measure the CP-violating trilinear gauge boson couplings. These results are compared with Standard Model expectations.Comment: Proceedings of the XXXth International Symposium on Multiparticle Dynamics (ISMD2000), 9-15 October 2000, Tihany, Hungary. 6 pages, 2 figures (LaTex, encapsulated PostScript

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