Related papers: Saturation scale from the Balitsky-Kovchegov equat…
We study the impact parameter dependence of solutions to the Balitsky-Kovchegov (BK) equation. We argue that if the kernel of the BK integral equation is regulated to cutoff infrared singularities, then it can be approximated by an equation…
In the previous work hep-ph/0112140, hep-ph/0204277, we showed that while the nonlinear QCD evolution equation of Balitsky and Kovchegov (BK) leads to saturation of the scattering amplitude locally in impact parameter space, it does not…
It was recently noticed that high-energy scattering processes in QCD have a stochastic nature. An event-by-event scattering amplitude is characterised by a saturation scale which is a random variable. The statistical ensemble of saturation…
Krylov complexity is a novel approach to study how an operator spreads over a specific basis. Recently, it has been stated that this quantity has a long-time saturation that depends on the amount of chaos in the system. Since this quantity…
Given a pure binomial ideal I in variables x_i, we define a new measure of the complexity of the saturation of I with respect to the product of the variables x_i, which we call the norm. We give a bound on the norm in terms of…
In this paper we found the parton densities at high energies. Their expressions stems from our attempts to reconcile the exact solution to the Balitsky-Kovchegov (BK) equation, which describes the rare fluctuation in the dipole-target…
A method how to construct Boolean-valued models of some fragments of arithmetic was developed in Krajicek (2011), with the intended applications in bounded arithmetic and proof complexity. Such a model is formed by a family of random…
We propose a general method to study the solutions to nonlinear QCD evolution equations, based on a deep analogy with the physics of traveling waves. In particular, we show that the transition to the saturation regime of high energy QCD is…
We propose a modified Balitskii-Fadin-Kuraev-Lipatov equation from the viewpoint of the resummation technique, which satisfies the unitarity bound. The idea is to relax the strong rapidity ordering and to restrict phase space for real gluon…
An approximate analytical solution of the Balitsky-Kovchegov (BK) equation using the homotopy perturbation method (HPM) is suggested in this work. We have carried out our work in perturbative QCD (pQCD) dipole picture of deep inelastic…
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…
The high-energy evolution in perturbative QCD suffers from a severe lack-of-convergence problem, due to higher order corrections enhanced by double and single transverse logarithms. We resum double logarithms to all orders within the…
We present a numerical study of solutions to the generalized Kadomtsev-Petviashvili equations with critical and supercritical nonlinearity for localized initial data with a single minimum and single maximum. In the cases with blow-up, we…
We present an extension to Kolmogorov's refined similarity hypothesis for universal fully developed turbulence. The extension is applied within Z. She and E. Leveque's multifractal model of inertial range scaling and its generalizations.…
We calculate inclusive photoproduction cross-sections for both proton and nuclei targets, using a saturation model derived from an approximate solution to the Balitsky-Kovchegov nonlinear evolution equation. This paper extends our…
The Smoluchowsky equation for a system of interacting Brownian particles in a temperature gradient is derived from the Kramers equation by means of a multiple time-scale method. The interparticle interactions are assumed to be represented…
In some applications, like some areas in stochastic geometry, a convenient change of variables involves spheres. In this review we summarize formulas of Blaschke-Petkantschin type, that help to pass from integration over $k$-tuples of…
We give a short proof of Bose Einstein Condensation of dilute Bose gases on length scales much longer than the Gross-Pitaevskii scale.
In this paper, we study a strong inverse approximation theorem and saturation order for the family of Kantorovich exponential sampling operators. The class of log-uniformly continuous and bounded functions, and class of log-H\"{o}lderian…
In this paper we address two questions: how energy conservation affects the solution to the non-linear equation, and how impact parameter dependence influences the inclusive production. Answering the first question we solve the modified BK…