Related papers: Unified derivation of evolution equations
An approach which unifies the Double Logarithmic Approximation at small x and the leading order DGLAP evolution of fragmentation functions at large x is presented. This approach reproduces exactly the Modified Leading Logarithm…
Starting from Boltzmann equation with relaxation time approximation for the collision term and using Chapman-Enskog like expansion for distribution function close to equilibrium, we derive hydrodynamic evolution equations for the…
We give a surface integral derivation of post-1-Newtonian translational equations of motion for a system of arbitrarily structured bodies, including the coupling to all the bodies' mass and current multipole moments. The derivation requires…
We expand our group classification of quasilinear evolution equations (Acta Appl.Math., v.69, 2001) to the case of general evolution equation in one spatial variable. This enables obtaining several new classes of evolution equations with…
We describe the N=1 supersymmetric evolution of the parton distributions with coupled gluinos and scalar quarks (Exact Supersymmetric Altarelli Parisi or ESAP). Superymmetric distributions are generated radiatively and studied as a function…
Riccati's differential equation is formulated as abstract equation in finite or infinite dimensional Banach spaces. Since the Riccati's differential equation with the Cole-Hopf transform shows a relation between the first order evolution…
Stochastic differential equations are widely used in various fields; in particular, the usefulness of duality relations has been demonstrated in some models such as population models and Brownian momentum processes. In this study, a…
The Gross-Pitaevskii equation with a local cubic nonlinearity that describes a many-dimensional system in an external field is considered in the framework of the complex WKB-Maslov method. Analytic asymptotic solutions are constructed in…
In the high energy regime, the proton structure consists of a very large number of particles called partons (quarks and gluons) that interact with each other, according to the theory of strong interactions, Quantum Chromodynamics (QCD).…
We present an efficient numerical solution of the DGLAP equations for single and double parton distribution functions (PDFs and DPDs), based on the Chebyshev interpolation of these functions. For PDF evolution, our method allows for a…
We introduce an $L_q(L_p)$-theory for the quasi-linear fractional equations of the type $$ \partial^{\alpha}_t u(t,x)=a^{ij}(t,x)u_{x^i x^j}(t,x)+f(t,x,u), \quad t>0, \,x\in \mathbf{R}^d. $$ Here, $\alpha\in (0,2)$, $p,q>1$, and…
We have shown that the small-$x$ evolution of the off-forward leading-log dipole scattering amplitudes, both pomeron and odderon, in the momentum space can be completely determined by the evolution of the respective forward amplitudes, with…
In this note we reexamine the possibility of extracting parton distribution functions from lattice simulations. We discuss the case of quasi-parton distribution functions, the possibility of using the reduced Ioffe-time distributions and…
We presented a general approach for obtaining the generalized transport equations with fractional derivatives by using the Liouville equation with fractional derivatives for a system of classical particles and Zubarev's nonequilibrium…
The Parton Branching (PB) approach describes the evolution of transverse momentum dependent (TMD) parton densities. We propose to extend the PB method by including TMD splitting functions, instead of the DGLAP splitting functions which…
Dynamics near and far away from thermal equilibrium is studied within the framework of Langevin equations. A stochasticity-dissipation relation is proposed to emphasize the equal importance of the stochastic and deterministic forces in…
We consider a derivation of the hierarchy of correlators of ordered exponentials directly from the Lipatov's effective action~\cite{LipatovEff} formulated in terms of interacting ordered exponentials~\cite{OurZub}. The derivation of the…
This paper focuses on a wide class of Collatz-type arithmetic dynamics, and presents a systematic derivation of recursive formulas and functional equations satisfied by the associated generating functions. The main tools belong to complex…
To study the heavy quark production processes, we use the transverse momentum dependent (TMD, or unintegrated) gluon distribution function in a proton obtained recently using the Kimber-Martin-Ryskin prescription from the Bessel-inspired…
In this paper, we consider an equation on random variables which can be reduced to the equation which describes the evolution of systems of fermions. We give some results of well-posedness for this equation on the spheres and torus of…