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By means of analytical calculations and numerical simulations we study the diffusion properties in quasi-two-dimensional structures with two exciton subsystems with an exchange between them. The experimental realisation is possible in systems where fast and slow exciton subsystems appear. For substantially different diffusion coefficients of the species the negative diffusion can be observed, if one measures the transport properties of only a single subsystem, just as was obtained in experimental studies for quasi-two-dimensional semiconductor systems. The initial transition from a fast subsystem to a slow one results in a delayed release of fast excitons in the area close to the original excitation spot. Hence, the signal from the fast excitons alone includes the delayed replenishment from the transition of slow quasi-particles. This is seen as the narrowing of the exciton density profile or decrease of mean-squared displacement which is then interpreted as a negative diffusion. The average diffusion coefficients for the combined population are analytically expressed through the diffusion coefficients of fast and slow excitons. Simple analytical expressions for effective diffusion coefficients obtained in limiting cases are of interest both for theoretical and experimental analysis of not only the exciton transport, but also for a variety of systems, where fast and slow moving subsystems are present., Comment: 12 pages, 4 figures

We show how two different mobile-immobile type models explain the observation of negative diffusion of excitons reported in experimental studies in quasi-two-dimensional semiconductor systems. The main reason for the effect is the initial trapping and a delayed release of free excitons in the area close to the original excitation spot. The density of trapped excitons is not registered experimentally. Hence, the signal from the free excitons alone includes the delayed release of not diffusing trapped particles. This is seen as the narrowing of the exciton density profile or decrease of mean-squared displacement which is then interpreted as a negative diffusion. The effect is enhanced with the increase of recombination intensity as well as the rate of the exciton-exciton binary interactions., Comment: 14 pages, 8 figures

We present a diffusion-based simulation and theoretical models for explanation of photoluminescence (PL) emission intensity in semiconductor nanoplatelets. It is shown that the shape of PL intensity curves can be reproduced by the interplay of recombination, diffusion and trapping of excitons. The emission intensity at short times is purely exponential and is defined by recombination. At long times it is governed by the release of excitons from surface traps and is characterized by a power-law tail. We show that the crossover from one limit to another is controlled by diffusion properties. This intermediate region exhibits a rich behaviour depending on the value of diffusivity. Proposed approach reproduces all the features of experimental curves measured for different nanoplatelet systems., Comment: 11 pages, 10 figures

We address the generic problem of random search for a point-like target on a line. Using the measures of search reliability and efficiency to quantify the random search quality, we compare Brownian search with L\'evy search based on long-tailed jump length distributions. We then compare these results with a search process combined of two different long-tailed jump length distributions. Moreover, we study the case of multiple targets located by a L\'evy searcher., Comment: 16 pages, 12 figures