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

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.

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Item Permalink: http://hdl.handle.net/21.11116/0000-0002-8071-D Version Permalink: http://hdl.handle.net/21.11116/0000-0003-7D35-6
Genre: Journal Article

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Lapolla, A.1, Author              
Godec, A.1, Author              
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1Research Group of Mathematical Biophysics, MPI for Biophysical Chemistry, Max Planck Society, ou_2396692              

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Free keywords: stochastic processes, occupation time functional, single- file diffusion, projection-induced memory, stochastic many-body systems, generating functional, large deviations
 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.

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Language(s): eng - English
 Dates: 2018-11-14
 Publication Status: Published online
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 Rev. Method: Peer
 Identifiers: DOI: 10.1088/1367-2630/aaea1b
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Title: New Journal of Physics
Source Genre: Journal
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Pages: 14 Volume / Issue: 20 Sequence Number: 113021 Start / End Page: - Identifier: -