Anomalous scaling at non-thermal fixed points of the sine-Gordon model

We extend the theory of non-thermal fixed points to the case of anomalously slow universal scaling dynamics according to the sine-Gordon model. This entails the derivation of a kinetic equation for the momentum occupancy of the scalar field from a non-perturbative two-particle irreducible effective action, which re-sums a series of closed loop chains akin to a large-$N$ expansion at next-to-leading order. The resulting kinetic equation is analyzed for possible scaling solutions in space and time that are characterized by a set of universal scaling exponents and encode self-similar transport to low momenta. Assuming the momentum occupancy distribution to exhibit a scaling form we can determine the exponents by identifying the dominating contributions to the scattering integral and power counting. If the field exhibits strong variations across many wells of the cosine potential, the scattering integral is dominated by the scattering of many quasiparticles such that the momentum of each single participating mode is only weakly constrained. Remarkably, in this case, in contrast to wave turbulent cascades, which correspond to local transport in momentum space, our results suggest that kinetic scattering here is dominated by rather non-local processes corresponding to a spatial containment in position space. The corresponding universal correlation functions in momentum and position space corroborate this conclusion. Numerical simulations performed in accompanying work yield scaling properties close to the ones predicted here.Comment: 20 pages, 2 figures. Hyperlinks complete

Far-from-equilibrium universal scaling dynamics in ultracold atomic systems and heavy-ion collisions

Classification and understanding of scaling solutions in closed quantum systems far from thermal equilibrium, known as nonthermal fixed points, are one of the open problems in nonequilibrium quantum many-body theory. The usual method involves searching for possible self-similar solutions to a (nonperturbative) evolution equation, e.g., Boltzmann or Kadanoff–Baym, starting from a far-from-equilibrium initial condition. In this work, we develop an alternative approach based on the correspondence between scaling and fixed points of the renormalization group. Using an ultracold Bose gas as an example we show how possible far-from-equilibrium scaling solutions can be systematically obtained by solving fixed-point renormalization-group equations. In the second part of this thesis, we investigate dynamics preceding a fully developed self-similar evolution. We use the Hamiltonian formulation of kinetic theory to perform a stability analysis of nonthermal fixed points in an expanding non-Abelian plasma characterized by the Fokker–Planck collision kernel. Employing an adiabatic expansion we develop a perturbation theory, which at next-to-leading order allows us to derive stability equations for scaling exponents and obtain the Lyapunov relaxation rates associated with a nonthermal fixed point

Stability analysis of nonthermal fixed points in longitudinally expanding kinetic theory

We use the Hamiltonian formulation of kinetic theory to perform a stability analysis of nonthermal fixed points in a non-Abelian plasma. We construct a perturbative expansion of the Fokker-Planck collision kernel in an adiabatic approximation and show that the (next-to-)leading order solutions reproduce the known nonthermal fixed point scaling exponents. Working at next-to-leading order, we derive the stability equations for scaling exponents and find the relaxation rate to the nonthermal fixed point. This approach provides the basis for an understanding of the prescaling phenomena observed in QCD kinetic theory and nonrelativistic Bose gas systems.We use the Hamiltonian formulation of kinetic theory to perform a stability analysis of non-thermal fixed points in a non-Abelian plasma. We construct a perturbative expansion of the Fokker-Planck collision kernel in an adiabatic approximation and show that the (next-to-)leading order solutions reproduce the known non-thermal fixed point scaling exponents. Working at next-to-leading order, we derive the stability equations for scaling exponents and find the relaxation rate to the non-thermal fixed point. This approach provides the basis for an understanding of the prescaling phenomena observed in QCD kinetic theory and non-relativistic Bose gas systems