Tagged particle in single-file diffusion with arbitrary initial conditions

Abstract

We compute the full probability distribution of the positions of a tagged particle exactly for given arbitrary initial positions of the particles and for general single-particle propagators. We consider the thermodynamic limit of our exact expressions in quenched and annealed settings. For a particular class of single-particle propagators, the exact formula is expressed in a simple integral form in the quenched case whereas in the annealed case, it is expressed as a simple combination of Bessel functions. In particular, we focus on the step and the power-law initial configurations. In the former case, a drift is induced even when the one-particle propagators are symmetric. On the other hand, in the later case the scaling of the cumulants of the position of the tracer becomes different than the uniform case. We provide numerical verifications of our results.

arXiv comment12 pages, 3 figures

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Cited by in corpus (13)

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• Tracer dynamics in one dimensional gases of active or passive particles
• Role of initial conditions in $1D$ diffusive systems: compressibility, hyperuniformity and long-term memory
• Effusion of stochastic processes on a line
• Generalized disorder averages and current fluctuations in run and tumble particles
• Uphill drift in the absence of current in single-file diffusion
• Tagged-Particle Statistics in Single-File Motion with Random-Acceleration and Langevin Dynamics
• Tracer dynamics in the active random average process
• Conserved densities of hard rods: microscopic to hydrodynamic solutions
• Exact fluctuation and long-range correlations in a single-file model under resetting
• PhD thesis "Extreme value statistics of strongly correlated systems: fermions, random matrices and random walks"
• Current fluctuations in finite-sized one-dimensional non-interacting passive and active systems