One-dimensional time-dependent distributions

A new derivation of two important one-dimensional time-dependent distributions for an infinite system of hard rods is presented. This derivation is simpler than previous derivations and it provides a direct physical interpretation of the individual terms in the final expressions. A new, more unusual distribution is also presented and discussed. Finally, an exact expression for the diffusion of a Brownian particle is obtained and compared with the exact expression for the self-diffusion coefficient.     

Generalized parton distributions

We discuss how generalized parton distributions (GPDs) enter in a variety of hard exclusive processes such as deeply virtual Compton scattering (DVCS) and hard meson electroproduction reactions on the nucleon. We show some key observables which are sensitive to the various hadron structure aspects of the GPDs, and discuss their experimental status.Received: 30 September 2002, Published online: 22 October 2003PACS: 13.60.Fz Elastic and Compton scattering - 13.60.Le Meson production - 12.38.Bx Perturbative calculations     

Power-law stellar distributions

The density profiles and other quantities of physical interest for spherically symmetric systems are computed by assuming that a collisionless stellar gas may relax to the non-Gaussian power-law distribution suggested by the nonextensive kinetic theory. There are two different classes of solutions. The first class behaves like a subset of the polytropic Lane–Emden spheres, whereas the second one corresponds to a transition between two different potytropic indices. Unlike the isothermal Maxwellian sphere, the total mass and sizes of both classes are finite for a large range of the nonextensive q-parameter.     

Relationship between degree-rank distributions and degree distributions of complex networks

Both the degree distribution and the degree-rank distribution, which is a relationship function between the degree and the rank of a vertex in the degree sequence obtained from sorting all vertices in decreasing order of degree, are important statistical properties to characterize complex networks. We derive an exact mathematical relationship between degree-rank distributions and degree distributions of complex networks. That is, for arbitrary complex networks, the degree-rank distribution can be derived from the degree distribution, and the reverse is true. Using the mathematical relationship, we study the degree-rank distributions of scale-free networks and exponential networks. We demonstrate that the degree-rank distributions of scale-free networks follow a power law only if scaling exponent λ>2. We also demonstrate that the degree-rank distributions of exponential networks follow a logarithmic law. The simulation results in the BA model and the exponential BA model verify our results.     

Quark-antiquark charge distributions

Monte Carlo simulation can provide a direct determination of the distribution of quarks inside hadrons. Such distributions are useful for a variety of purposes, including the study of confinement. We discuss the theoretical and practical issues involved. A detailed study of two-dimensional QCD is described.     

Non-equilibrated post-freeze-out distributions

We discuss freeze-out on the hypersurface with time-like normal vector, trying to answer how realistic it is to assume thermal post-freeze-out distributions for measured hadrons. Using simple kinetic models for gradual freeze-out we are able to generate a thermal post-FO distribution, but only in a highly simplified situation. In a more advanced model, taking into account rescattering and re-thermalization, the post-FO distribution gets more complicated. The resulting particle distributions are in qualitative agreement with the experimentally measured pion spectra. Our study also shows that the obtained post-FO distribution functions, although analytically very different from the Jüttner distribution, do look pretty much like thermal distributions in some range of the parameters.Received: 8 April 2003, Revised: 5 June 2003, Published online: 15 August 2003     

Generalized parton distributions

An introductory review of generalized parton distributions (GPDs) is given.Received: 1 November 2002, Published online: 15 July 2003PACS: 13.40.Gp Electromagnetic form factors - 13.60.Fz Elastic and Compton scattering - 13.60.Hb Total and inclusive cross-sections (including deep-inelastic processes)     

Many-body work distributions

The work distribution function for a non-relativistic, non-interacting quantum many-body system interacting with classical external sources is investigated. Exact expressions for the characteristic function corresponding to the work distribution function is obtained for arbitrary switching function and coupling functions. The many-body frequencies are assumed to be generally time-dependent in order to take into account the possibility of moving the boundaries of the system in a predefined process linking the characteristic function to the fluctuation-induced energies in confined geometries. Some limiting cases are considered and discussed.     

Nuclear matter distributions

The present knowledge of the distribution of neutrons and protons in the nucleus is reviewed. The distributions calculated by the single-particle potential method and from the Hartree-Fock theory are compared with the experimental data. Particular attention is paid to the hyperfine anomaly and the isotope shifts, and to the connection with the distribution of nuclear magnetisation.     

Pionic parton distributions

The gluon and sea distributions of the pion are uniquely determined by the requirement of avalence-like structure of the input parton distributions at some low resolution scale. These (dynamical) results are obtained with practically no free parameters, just using the experimentally determined pionic valence distribution combined with the constraints for the pionic gluon distribution provided by direct-γ data. Simple parametrizations of the resulting parton distributions are presented in the range 10^?5?x<1 and 0.3?Q ²?10⁸ GeV² as obtained from the leading-and higher-order evolution equations.     

On the toroidal distributions

The so called toroidal distributions were obtained using the method previously employed to derive the other decompositions of the electric type transition operator used in literature. Some aspects of toroidal distributions are discussed. The condition is given which has to be imposed on the decomposition generating function in order that the Siegert's theorem holds.     

On Lorentz invariant distributions

n-point Lorentz invariant tempered distributions with the supports for one-point only in are described.     

Meson distributions in photoproduction

Extension of the nova model is applied to γ + p → π + anything. The concept of a photon is motivated from vector dominance, and the parameters describing the production of photon novas are estimated from hadron results. The model is essentially without arbitrary parameters. We compare with inclusive and exclusive data at 9.3 GeV/c, where we find excellent agreement. Predictions for 20 GeV/c are also presented.     

Density distributions in nuclei

Density distribution across the nuclear surface is obtained in the approximation of relatively sharp nuclear edge. It is used to determine dynamical parts of the density relevant to density vibration resonances. Results of the simple calculations are in close agreement with detailed microscopic theories.     

Double-parton distributions in QCD

It is shown that the factorization hypothesis, which is usually applied to two-parton distributions at the present time in analyzing experimental data on double parton scattering, is in an obvious contradiction with the QCD evolution equations. The predictions of QCD for basic properties of two-parton distribution are discussed.     

Calculating heavy quark distributions

A systematic calculation of the evolution of parton distribution functions including the effects of heavy-quark masses is presented. The method involves the use of a special renormalization scheme which ensures ordinary massless evolution with the correct number of active quark flavors at all stages, and specifies appropriate matching conditions at thresholds. This method is applicable to all orders of the perturbation expansion in principle, and it is simple to implement in practice. Results of this calculation using known distributions at low energies as input are examined and compared with published results. The heavy-quark distribution functions are found to be about a factor of two larger than the well-known EHLQ results.     

First-passage time distributions for linear chain segments with general site-dependent waiting-time distributions

First-passage time distributions (FPTD) of the arrival of a walk at a terminal site of a finite linear chain are considered, where the individual transition processes between the sites are specified by rather general waiting-time distributions. An exact expression for the first-passage time distribution can be given in Laplace space in terms of finite continued fractions. The circumstances under which the calculation of FPTD by this technique offers advantages over conventional calculations via master equations are discussed and possible applications to systems of biophysical interest are indicated. Presented at the Czech-Israeli-German Symposium “Dynamical Processes in Condensed Molecular Systems”, Prague, Czech Republic, 26–30 May 1997.