A ubiquitous observation in crowded cell membranes is that molecular transport does not follow Fickian diffusion but exhibits subdiffusion. The microscopic origin of such a behaviour is not understood and highly debated. Here we discuss the spatio-temporal dynamics for two models of subdiffusion: fractional Brownian motion and hindered motion due to immobile obstacles. We show that the different microscopic mechanisms can be distinguished using fluorescence correlation spectroscopy (FCS) by systematic variation of the confocal detection area. We provide a theoretical framework for space-resolved FCS by generalising FCS theory beyond the common assumption of spatially Gaussian transport. We derive a master formula for the FCS autocorrelation function, from which it is evident that the beam waist of an FCS experiment is a similarly important parameter as the wavenumber of scattering experiments. These results lead to scaling properties of the FCS correlation for both models, which are tested by in silico experiments. Further, our scaling prediction is compatible with the FCS half-value times reported by Wawrezinieck et al. [Biophys. J. 89, 4029 (2005)] for in vivo experiments on a transmembrane protein.

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The goals of discovering quantum radiation dynamics in high-intensity laser-plasma interactions and engineering new laser-driven high-energy particle sources both require accurate and robust predictions. Experiments rely on particle-in-cell simulations to predict and interpret outcomes, but unknowns in modeling the interaction limit the simulations to qualitative predictions, too uncertain to test the quantum theory. To establish a basis for quantitative prediction, we introduce a 'jet' observable that parameterizes the emitted photon distribution and quantifies a highly directional flux of high-energy photon emission. Jets are identified by the observable under a variety of physical conditions and shown to be most prominent when the laser pulse forms a wavelength-scale channel through the target. The highest energy photons are generally emitted in the direction of the jet. The observable is compatible with characteristics of photon emission from quantum theory. This work offers quantitative guidance for the design of experiments and detectors, offering a foundation to use photon emission to interpret dynamics during high-intensity laser-plasma experiments and validate quantum radiation theory in strong fields.