Active Brownian Particles. From Individual to Collective Stochastic Dynamics

We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of such self-propelled entities in the framework of statistical mechanics. Examples of such active units in complex physico-chemical and biological systems are chemically powered nano-rods, localized patterns in reaction-diffusion system, motile cells or macroscopic animals. Based on the description of individual motion of point-like active particles by stochastic differential equations, we discuss different velocity-dependent friction functions, the impact of various types of fluctuations and calculate characteristic observables such as stationary velocity distributions or diffusion coefficients. Finally, we consider not only the free and confined individual active dynamics but also different types of interaction between active particles. The resulting collective dynamical behavior of large assemblies and aggregates of active units is discussed and an overview over some recent results on spatiotemporal pattern formation in such systems is given.Comment: 161 pages, Review, Eur Phys J Special-Topics, accepte

Nonlinear optics and saturation behavior of quantum dot samples under continuous wave driving

The nonlinear optical response of self-assembled quantum dots is relevant to the application of quantum dot based devices in nonlinear optics, all-optical switching, slow light and self-organization. Theoretical investigations are based on numerical simulations of a spatially and spectrally resolved rate equation model, which takes into account the strong coupling of the quantum dots to the carrier reservoir created by the wetting layer states. The complex dielectric susceptibility of the ground state is obtained. The saturation is shown to follow a behavior in between the one for a dominantly homogeneously and inhomogeneously broadened medium. Approaches to extract the nonlinear refractive index change by fringe shifts in a cavity or self-lensing are discussed. Experimental work on saturation characteristic of InGa/GaAs quantum dots close to the telecommunication O-band (1.24-1.28 mm) and of InAlAs/GaAlAs quantum dots at 780 nm is described and the first demonstration of the cw saturation of absorption in room temperature quantum dot samples is discussed in detail