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We examine numerically different zero-dimensional reaction-diffusion processes as candidate toy models for high-energy QCD evolution. Of the models examined -- Reggeon Field Theory, Directed Percolation and Reversible Processes -- only the…
We shall deal with the periodic problem for nonlinear perturbations of abstract hyperbolic evolution equations generating an evolution system of contractions. We prove an averaging principle for the translation along trajectories operator…
This paper investigates the asymptotic behaviour of solutions of periodic evolution equations. Starting with a general result concerning the quantified asymptotic behaviour of periodic evolution families we go on to consider a special class…
Evolution equations for multiplicities in QCD cascades can, both in the parton and dipole picture, be used to estimate corrections beyond the formal accuracy of the modified leading log approximation (MLLA). The differences between the two…
The problem of computing differential constraints for a family of evolution PDEs is discussed from a constructive point of view. A new method, based on the existence of generalized characteristics for evolution vector fields, is proposed in…
The nonlinear Balitsky-Kovchegov equation at small x is solved numerically, incorporating impact parameter dependence. Confinement is modeled by including effective gluon mass in the dipole evolution kernel, which regulates the splitting of…
The evolution of non-hydrodynamic slow processes near the QCD critical point is explored with the novel Hydro+ framework, which extends the conventional hydrodynamic description by coupling it to additional explicitly evolving slow modes…
We evaluate the complete leading-order evolution kernels for the chiral-odd twist-3 distributions $e(x)$ and $\widetilde h_L(x)$ of the nucleon. We establish the connection between the evolution equations in light-cone position and…
We study hyperbolic systems of one-dimensional partial differential equations under general, possibly non-local boundary conditions. A large class of evolution equations, either on individual 1-dimensional intervals or on general networks,…
Coherence phenomena, and the non-universality of parton structure of the effective Pomeron are explained. New hard phenomena directly calculable in QCD such as diffractive electroproduction of states with $M^2\ll Q^2$ as well as new options…
We apply methods of dynamical systems to study the behaviour of the Randall-Sundrum models. We determine evolutionary paths for all possible initial conditions in a 2-dimensional phase space and we investigate the set of accelerated models.…
We study the impact of the QCD DGLAP evolution on the geometric scaling of the gluon distributions which is expected to hold at small x within the saturation models. To this aim we solve the DGLAP evolution equations with the initial…
The corrections of gluon fusion to the DGLAP and BFKL equations are discussed in a united partonic framework. The resulting nonlinear evolution equations are the well-known GLR-MQ-ZRS equation and a new evolution equation. Using the…
General implications of existence of non-perturbative scales and hadronic sub-structure for high energy processes are discussed. We propose that the dependence of the cross section of $\bar q q$ dipoles on their size d should deviate from…
We propose a computer-assisted approach to studying the effective continuum behavior of spatially discrete evolution equations. The advantage of the approach is that the "coarse model" (the continuum, effective equation) need not be…
The asymptotic collinear factorisation theorem, which holds for diffractive deep-inelastic scattering, has important modifications in the sub-asymptotic HERA regime. We use perturbative QCD to quantify these modifications. The diffractive…
High energy scattering is considered within the framework of the QCD dipole model formulated as a classical branching process. Starting from Mueller's generating functional we derive the high energy evolution law for the scattering…
Generalized parton distributions (GPDs) characterize the 3-dimensional structure of hadrons, combining information about their internal quark and gluon longitudinal momentum distributions and transverse position within the hadron. The…
We study the evolution behavior of generalized parton distributions at small longitudinal momentum fraction. Particular attention is paid to the ratio of a generalized parton distribution and its forward limit, to the mixing between quarks…
We provide a concise introduction to the symmetry approach to integrability. Some results on integrable evolution and systems of evolution equations are reviewed. Quasi-local recursion and Hamiltonian operators are discussed. We further…