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Unfolding tagged particle histories in single-file diffusion: Exact single- and two-tag local times beyond large deviation theory.

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Lapolla,  A.
Research Group of Mathematical Biophysics, MPI for Biophysical Chemistry, Max Planck Society;

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Godec,  A.
Research Group of Mathematical Biophysics, MPI for Biophysical Chemistry, Max Planck Society;

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Citation

Lapolla, A., & Godec, A. (2018). Unfolding tagged particle histories in single-file diffusion: Exact single- and two-tag local times beyond large deviation theory. New Journal of Physics, 20: 113021. doi:10.1088/1367-2630/aaea1b.


Cite as: http://hdl.handle.net/21.11116/0000-0002-8071-D
Abstract
Strong positional correlations between particles render the diffusion of a tracer particle in a single file anomalous and non-Markovian. While ensemble average observables of tracer particles are nowadays well understood, little is known about the statistics of the corresponding functionals, i.e. the time-average observables. It even remains unclear how the non-Markovian nature emerges from correlations between particle trajectories at different times. Here, we first present rigorous results for fluctuations and two-tag correlations of general bounded functionals of ergodic Markov processes with a diagonalizable propagator. They relate the statistics of functionals on arbitrary time-scales to the relaxation eigenspectrum. Then we study tagged particle local times—the time a tracer particle spends at some predefined location along a single trajectory up to a time t. Exact results are derived for one- and two-tag local times, which reveal how the individual particles' histories become correlated at higher densities because each consecutive displacement along a trajectory requires collective rearrangements. Our results unveil the intricate meaning of projection-induced memory on a trajectory level, invisible to ensemble-average observables, and allow for a detailed analysis of single-file experiments probing tagged particle exploration statistics.