相关论文: QCD Saturation Equations including Dipole-Dipole C…

We establish the dual notions of scaling and saturation from geometric control theory in an infinite-dimensional setting. This generalization is applied to the low-mode control problem in a number of concrete nonlinear partial differential…

It is shown in this paper that the QCD equations for dipole density have the natural solution: the 'fan' diagrams of the Pomeron calculus. We found the dipole densities comparing the analytic solution to the Balitsky-Kovchegov (BK) equation…

Linear and non-linear QCD evolutions at high energy suffer from severe issues related to convergence, due to higher order corrections enhanced by large double and single transverse logarithms. We resum double logarithms to all orders by…

We study in this paper solutions to several kinds of linear bimatrix equations arising from pole assignment and stability analysis of complex-valued linear systems, which have several potential applications in control theory, particularly,…

We reproduce the DIS measurements of the proton structure function at high energy from the dipole model in momentum space. To model the dipole-proton forward scattering amplitude, we use the knowledge of asymptotic solutions of the…

The model of a multi-level system interacting with several reservoirs is considered. The exact reduced density matrix evolution could be obtained for this model without Markov approximation. Namely, this evolution is fully defined by the…

The Balitsky--Kovchegov (BK) evolution equation in its resummed integral form as obtained in JHEP 1202 (2012) 117 and arXiv:1206.1223 is considered. We solve it numerically and compare to the unresummed BK equation formulated as an integral…

We investigate the Balitsky-Kovchegov (BK) equation for D=3 space-time dimensions, corresponding to one transverse coordinate, and we show that it can be solved analytically. The explicit solutions are found in the linear approximation and…

The recently proposed nonlinear evolution equation \cite{Kutak:2013hda} for unintegrated gluon densities valid for large values of the QCD coupling constant $\bar{\alpha} _s$ is presented. In particular we outline its derivation, numerical…

We study almost prime solutions of systems of Diophantine equations in the Birch setting. Previous work shows that there exist integer solutions of size B with each component having no prime divisors below $B^{1/u}$, where $u=c_0n^{3/2}$,…

To sum high energy leading logarithms in a consistent way, one has to impose the strong ordering in both projectile rapidity and dense target rapidity simultaneously, which results in a kinematically improved Balitsky-Kovchegov(BK)…

We derive generalization of the Balitsky-Kovchegov (BK) equation for a dipole, which consists of a parton and an antiparton of arbitrary charge. At first, we develop one method of indexless transformation of color expressions. The method is…

In this paper the inverse scattering problem for the nonstationary Dirac-type system on the whole plane was considered. A nonlinear evolution sytem of equation related to nonstationary Dirac-type system is introduced and the solviblity of…

A unitarized BFKL equation incorporating shadowing and antishadowing corrections of the gluon recombination is proposed. This equation reduces to the Balitsky-Kovchegov evolution equation near the saturation limit. We find that the…

We present a short overview of saturation physics followed by a summary of the recent progress in our understanding of nonlinear small-$x$ evolution. Topics include McLerran-Venugopalan model, Glauber-Mueller approximation, nonlinear…

We demonstrate that the dipole-hadron cross-section computed from the non-linear evolution equation for the Colour Glass Condensate saturates the Froissart bound in the case of a fixed coupling and for a small dipole (Q^2 >>…

Convergence of a full discretization of a second order stochastic evolution equation with nonlinear damping is shown and thus existence of a solution is established. The discretization scheme combines an implicit time stepping scheme with…

We perform a global fit to the structure function F_2 measured in lepton-proton experiments at small values of Bjorken-x, x\le 0.01, for all experimentally available values of Q^2, 0.045 GeV^2\le Q^2 \le 800 GeV^2. We show that the recent…

We use the BBGKY hierarchy equations to calculate, perturbatively, the lowest order nonlinear correction to the two point correlation and the pair velocity for Gaussian initial conditions in a critical density matter dominated cosmological…

We show that the GBW saturation model provides an exact solution to the one dimensional linear transport equation. We also show that it is motivated by the BK equation considered in the saturated regime when the diffusion and the splitting…