Molecular transport in living systems regulates numerous processes underlying biological function.\ud Although many cellular components exhibit anomalous diffusion, only recently has the subdiffusive\ud motion been associated with nonergodic behavior. These findings have stimulated new questions for their\ud implications in statistical mechanics and cell biology. Is nonergodicity a common strategy shared by living\ud systems? Which physical mechanisms generate it? What are its implications for biological function? Here,\ud we use single-particle tracking to demonstrate that the motion of dendritic cell-specific intercellular\ud adhesion molecule 3-grabbing nonintegrin (DC-SIGN), a receptor with unique pathogen-recognition\ud capabilities, reveals nonergodic subdiffusion on living-cell membranes In contrast to previous studies, this\ud behavior is incompatible with transient immobilization, and, therefore, it cannot be interpreted according to\ud continuous-time random-walk theory. We show that the receptor undergoes changes of diffusivity,\ud consistent with the current view of the cell membrane as a highly dynamic and diverse environment.\ud Simulations based on a model of an ordinary random walk in complex media quantitatively reproduce all\ud our observations, pointing toward diffusion heterogeneity as the cause of DC-SIGN behavior. By studying\ud different receptor mutants, we further correlate receptor motion to its molecular structure, thus establishing\ud a strong link between nonergodicity and biological function. These results underscore the role of disorder\ud in cell membranes and its connection with function regulation. Because of its generality, our approach\ud offers a framework to interpret anomalous transport in other complex media where dynamic heterogeneity\ud might play a major role, such as those found, e.g., in soft condensed matter, geology, and ecology.Peer ReviewedPostprint (published version

Non-ergodicity observed in single-particle tracking experiments is usually modeled by transient trapping rather than spatial disorder. We introduce models of a particle diffusing in a medium consisting of regions with random sizes and random diffusivities. The particle is never trapped, but rather performs continuous Brownian motion with the local diffusion constant. Under simple assumptions on the distribution of the sizes and diffusivities, we find that the mean squared displacement displays subdiffusion due to non-ergodicity for both annealed and quenched disorder. The model is formulated as a walk continuous in both time and space, similar to the Lévy walk.PACS numbers: 05.40.Fb,87.10.Mn,87.15.Vv Disordered systems exhibiting subdiffusion have been studied intensively for decades [1][2][3][4][5]. In these systems the ensemble averaged mean squared displacement (EMSD) grows for large times aswhereas normal diffusion has β = 1. A broad class of systems show weak ergodicity breaking, that is, the EMSD and the time averaged mean squared displacement (TMSD) differ. The prototypical framework for describing non-ergodic subdiffusion is the heavy-tailed continuous-time random walk (CTRW) [6][7][8], in which a particle takes steps at random time intervals that are independently distributed with densityψ(τ ) has infinite mean, which leads to a subdiffusive EMSD β = α. Furthermore, the CTRW shows weak ergodicity breaking because the particle experiences trapping times on the order of the observation time T no matter how large T is. The CTRW was introduced to describe charge carriers in amorphous solids [8], and has found wide application since. Recently, there has been a surge of work on the CTRW [9-12], triggered by single particle tracking experiments in biological systems [13][14][15][16][17] that display signatures of non-ergodicity. A different approach to subdiffusion is to assume a deterministic diffusivity (i.e. diffusion coefficient) that is inhomogeneous in time [18,19], or space [20][21][22][23][24]. But in fact, the anomalous diffusion in these works is also nonergodic. Formulating models of inhomogeneous diffusivity is timely and important, given that recently measured spatial maps in the cell membrane often show patches of strongly varying diffusivity [25][26][27][28][29][30]. The presence of randomness in these experimental maps inspired us to consider disordered media. Thus, in this manuscript, we introduce a class of models of ordinary diffusion with a diffusivity that varies randomly but is constant on patches of random sizes. We call these models random patch models or just patch models. These models show non-ergodic subdiffusion, due to the diffusivity effectively changing at random times with a heavy-tailed distribution like that in (2) [31]. Note that ergodicity breaking is usually ascribed to energetic disorder that immobilizes the particle, e.g. via transient chemical binding [8,32,33]. But, in the patch models discussed here the particle constantly undergoes Brownian motion. The anomaly is i...

Abstract. The concentration and distribution of quantum entanglement is an essential ingredient in emerging quantum information technologies. Much theoretical and experimental effort has been expended in understanding how to distribute entanglement in one-dimensional networks. However, as experimental techniques in quantum communication develop, protocols for multi-dimensional systems become essential. Here, we focus on recent theoretical developments in protocols for distributing entanglement in regular and complex networks, with particular attention to percolation theory and network-based error correction.

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We present percolation strategies based on multipartite measurements to propagate entanglement in quantum networks. We consider networks spanned on regular lattices whose bonds correspond to pure but non-maximally entangled pairs of qubits, with any quantum operation allowed at the nodes. Despite significant effort in the past, improvements over naive (classical) percolation strategies have been found for only few lattices, often with restrictions on the initial amount of entanglement in the bonds. In contrast, multipartite entanglement percolation outperform the classical percolation protocols, as well as all previously known quantum ones, over the entire range of initial entanglement and for every lattice that we considered.Comment: revtex4, 4 page