Related papers: From QCD at high energy to statistical physics and…
In these lecture notes we discuss recent progress in the rigorous derivation of effective evolution equations for the description of the dynamics of quantum mechanical many-body systems.
I discuss recent developments in the QCD cascade formalism. I focus on the importance of and uncertainties in higher order corrections to the Modified Leading Log approximation for final-state radiation. I also talk about the CCFM and LDC…
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…
The main topic of this thesis is the analysis of evolution equations reflecting issues in ecology and population dynamics. In mathematical modelling, the impact of environmental elements and the interaction between species is read into the…
Evolution equations describe the effect of consecutively integrating out all quantum fluctuations with momenta larger than some infrared cutoff scale k. We develop a formalism for the introduction of collective degrees of freedom at some…
The article provides an overview of some advances in the mathematical understanding of the nature of the kinetic equations of quantum systems of many particles. The fundamental equations of modern mathematical physics are studied, in…
We analyse the evolution of cosmological perturbations which leads to the formation of large isolated voids in the Universe. We assume that initial perturbations are spherical and all components of the Universe (radiation, matter and dark…
What features characterise complex system dynamics? Power laws and scale invariance of fluctuations are often taken as the hallmarks of complexity, drawing on analogies with equilibrium critical phenomena[1-3]. Here we argue that slow,…
The next-to-leading order (NLO) Balitsky-Kovchegov (BK) equation describing the high-energy evolution of the scattering between a dilute projectile and a dense target suffers from instabilities unless it is supplemented by a proper…
The QCD structure of the electron is defined and calculated. The leading order splitting functions are extracted, showing an important contribution from $\gamma$-$Z$ interference. Leading logarithmic QCD evolution equations are constructed…
We explore several models of QCD evolution equations simplified by considering only the rapidity dependence of dipole scattering amplitudes, while provisionally neglecting their dependence on transverse coordinates. Our main focus is on the…
We carry out a comprehensive study of the dynamics of large-scale perturbations in quintessence scenarios. We model the contents of the Universe by a perfect fluid with equation of state w_f and a scalar field Q with potential V(Q). We are…
The strong coupling $\alpha_s$ is determined with high precision from fits to lattice QCD simulations on the static energy. Our theoretical setup relies on R-improving the three-loop fixed-order prediction for the static energy by removing…
Scattering amplitudes in QCD exhibit a definite RG flow with energy towards the unitarity limit. In this paper we put forward an evolution equation which allows one to modify continuously the pre-asymptotic RG flow towards "saturation" of…
In this talk, we briefly review the current understanding of the behavior of the QCD equation of state throughout the phase diagram. Special emphasis is given to regions of phenomenological interest, and a number of important open questions…
We study the dynamics of states perturbatively expanded about a harmonic system of loop quantum cosmology, exhibiting a bounce. In particular, the evolution equations for the first and second order moments of the system are analyzed. These…
The non-linear evolution of a stratified perturbation in a three dimensional expanding Universe is considered. A general Lagrangian scheme (Q model) is introduced and numerical investigations are performed. The asymptotic contraction of the…
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…
A system of two cubic reaction-diffusion equations for two independent gene frequencies arising in population dynamics is studied. Depending on values of coefficients, all possible Lie and $Q$-conditional (nonclassical) symmetries are…
Inhomogeneous cosmological perturbation equations are derived in loop quantum gravity, taking into account corrections in particular in gravitational parts. This provides a framework for calculating the evolution of modes in structure…