We develop a transport approach for heavy quarks in a quark-gluon plasma, which is based on improved binary collision rates taking into account quantum statistics, the running of the QCD coupling and an effective screening mass adjusted to hard-thermal loop calculations. We quantify the effects of in-medium collisions by calculating the heavy flavor nuclear modification factor and the elliptic flow for RHIC energies, which are comparable to radiative effects. We also derive an analytic formula for the mean collisional energy loss of an energetic heavy quark in a streaming quark gluon plasma.

We present an efficient method for simulating a stationary Gaussian noise with an arbitrary covariance function and then study numerically the impact of time-correlated noise on the time evolution of a 1 + 1 dimensional generalized Langevin equation by comparing also to analytical results. Finally, we apply our method to the generalized Langevin equation with an external harmonic and double-well potential.

An overview is presented of transverse momentum distributions of particles at the LHC using the Tsallis distribution. The use of a thermodynamically consistent form of this distribution leads to an excellent description of charged and identified particles. The values of the Tsallis parameter q are truly remarkably consistent.

Particles and fields are standard components in numerical calculations like transport simulations in nuclear physics and have well understood dynamics. Still, a common problem is the interaction between particles and fields due to their different formal description. Particle interactions are discrete, point-like events while field dynamics is described with continuous partial-differential equations of motion. A workaround is the use of effective theories like the Langevin equation with the drawback of energy conservation violation. We present a method, which allows to model noncontinuous interactions between particles and scalar fields, allowing us to simulate scatteringlike interactions which exchange discrete "quanta" of energy and momentum between fields and particles while obeying energy and momentum conservation and allowing control over interaction strengths and times. In this paper we apply this method to different model systems, starting with a simple harmonic oscillator, which is damped by losing discrete energy quanta. The second and third system consists of an oscillator and a one-dimensional field, which are damped via discrete energy loss and are coupled to a stochastic force, leading to equilibrium states which correspond to statistical Langevin-like systems. The last example is a scalar field in (1+3) space-time dimensions, which is coupled to a microcanonical ensemble of particles by incorporating particle production and annihilation processes. Obeying the detailed-balance principle, the system equilibrates to thermal and chemical equilibrium with dynamical fluctuations on the fields, generated dynamically by the discrete interactions.

We apply a Boltzmann approach to the kinetic regime of a relativistic Bose-Einstein condensate of scalar bosons by decomposing the one-particle distribution function in a condensate part and a non-zero momentum part of excited modes, leading to a coupled set of evolution equations which are then solved efficiently with an adaptive higher order Runge-Kutta scheme. We compare our results to the partonic cascade Monte-Carlo simulation BAMPS for a critical but far from equilibrium case of massless bosons. Motivated by the color glass condensate initial conditions in QCD with a strongly overpopulated initial glasma state, we also discuss the time evolution starting from an overpopulated initial distribution function of massive scalar bosons. In this system a self-similar evolution of the particle cascade with a non-relativistic turbulent scaling in the infrared sector is observed as well as a relativistic exponent for the direct energy cascade, confirming a weak wave turbulence in the ultraviolet region.