Gluon Shadowing and Heavy Flavor Production off Nuclei

Gluon shadowing which is the main source of nuclear effects for production of heavy flavored hadrons, remains unknown. We develop a light-cone dipole approach aiming at simplifying the calculations of nuclear shadowing for heavy flavor production, as well as the cross section which does not need next-to-leading and higher order corrections. A substantial process dependence of gluon shadowing is found at the scale of charm mass manifesting a deviation from QCD factorization. The magnitude of the shadowing effect correlates with the symmetry properties and color state of the produced c-cbar pair. It is about twice as large as in DIS, but smaller than for charmonium production. The higher twist shadowing correction related to a nonzero size of the c-cbar pair is not negligible and steeply rises with energy. We predict an appreciable suppression by shadowing for charm production in heavy ion collisions at RHIC and a stronger effect at LHC. At the same time, we expect no visible difference between nuclear effects for minimal bias and central collisions, as is suggested by recent data from the PHENIX experiment at RHIC. We also demonstrate that at medium high energies when no shadowing is possible, final state interaction may cause a rather strong absorption of heavy flavored hadrons produced at large x_F.Comment: Preprint NSF-ITP-02-40, ITP, UCSB, Santa Barbara; Latex 52 pages and 8 figure

Fractional Generalization of Gradient Systems

We consider a fractional generalization of gradient systems. We use differential forms and exterior derivatives of fractional orders. Examples of fractional gradient systems are considered. We describe the stationary states of these systems.Comment: 11 pages, LaTe

Fractional Variations for Dynamical Systems: Hamilton and Lagrange Approaches

Fractional generalization of an exterior derivative for calculus of variations is defined. The Hamilton and Lagrange approaches are considered. Fractional Hamilton and Euler-Lagrange equations are derived. Fractional equations of motion are obtained by fractional variation of Lagrangian and Hamiltonian that have only integer derivatives.Comment: 21 pages, LaTe

Path Integral for Quantum Operations

In this paper we consider a phase space path integral for general time-dependent quantum operations, not necessarily unitary. We obtain the path integral for a completely positive quantum operation satisfied Lindblad equation (quantum Markovian master equation). We consider the path integral for quantum operation with a simple infinitesimal generator.Comment: 24 pages, LaTe

Dynamics of Fractal Solids

We describe the fractal solid by a special continuous medium model. We propose to describe the fractal solid by a fractional continuous model, where all characteristics and fields are defined everywhere in the volume but they follow some generalized equations which are derived by using integrals of fractional order. The order of fractional integral can be equal to the fractal mass dimension of the solid. Fractional integrals are considered as an approximation of integrals on fractals. We suggest the approach to compute the moments of inertia for fractal solids. The dynamics of fractal solids are described by the usual Euler's equations. The possible experimental test of the continuous medium model for fractal solids is considered.Comment: 12 pages, LaTe