Time-dependent reactivity for diffusion-controlled annihilation and coagulation in two dimensions

Picosecond time-resolved photon antibunching measures nanoscale exciton motion and the true number of chromophores

The particle-like nature of light becomes evident in the photon statistics of fluorescence from single quantum systems as photon antibunching. In multichromophoric systems, exciton diffusion and subsequent annihilation occurs. These processes also yield photon antibunching but cannot be interpreted reliably. Here we develop picosecond time-resolved antibunching to identify and decode such processes. We use this method to measure the true number of chromophores on well-defined multichromophoric DNA-origami structures, and precisely determine the distance-dependent rates of annihilation between excitons. Further, this allows us to measure exciton diffusion in mesoscopic H- and J-type conjugated-polymer aggregates. We distinguish between one-dimensional intra-chain and three-dimensional inter-chain exciton diffusion at different times after excitation and determine the disorder-dependent diffusion lengths. Our method provides a powerful lens through which excitons can be studied at the single-particle level, enabling the rational design of improved excitonic probes such as ultra-bright fluorescent nanoparticles and materials for optoelectronic devices.

Aggregation process on complex networks

We study the dynamics of the aggregation of particles and the evolution of the mass distribution, on a complex network which is built following the Watts-Strogatz model. The particles perform random walks following the links on the network, and aggregate when they meet other particles. On disordered networks the density of particles decays as t(-1), while on regular networks it decays as t(-1/2). For intermediate levels of network disorder the dynamics follows that of regular networks at intermediate density, and for low density the disorder of the network becomes relevant and the density decays as t(-1). The crossover time between these two regimes scales with network disorder as t approximately p(-2). We study also an annealed model for the aggregation process, in which the quenched disorder of the network is replaced by stochastic long range jumps in the particle dynamics. The annealed model is found to obey a different scaling with network disorder, with a crossover time t approximately p(-1).

Exact solutions to nonlinear nonautonomous space-fractional diffusion equations with absorption

We analyze a nonlinear fractional diffusion equation with absorption by employing fractional spatial derivatives and obtain some more exact classes of solutions. In particular, the diffusion equation employed here extends some known diffusion equations such as the porous medium equation and the thin film equation. We also discuss some implications by considering a diffusion coefficient D(x,t)=D(t)/x/(-theta) (theta in R) and a drift force F=-k(1)(t)x+k(alpha)x/x/(alpha-1). In both situations, we relate our solutions to those obtained within the maximum entropy principle by using the Tsallis entropy.

Anomalous diffusion with absorption: exact time-dependent solutions

Recently, analytical solutions of a nonlinear Fokker-Planck equation describing anomalous diffusion with an external linear force were found using a nonextensive thermostatistical Ansatz. We have extended these solutions to the case when an homogeneous absorption process is also present. Some peculiar aspects of the interrelation between the deterministic force, the nonlinear diffusion, and the absorption process are discussed.