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Role of initial conditions in $1D$ diffusive systems: compressibility, hyperuniformity and long-term memory

Accepted version
Peer-reviewed

Type

Article

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Authors

Banerjee, Tirthankar 
Jack, Robert L 
Cates, Michael E 

Abstract

We analyse the long-lasting effects of initial conditions on fluctuations in one-dimensional diffusive systems. We consider both the fluctuations of current for non-interacting diffusive particles starting from a step-like initial density profile, and the mean-square displacement of tracers in homogeneous systems with single-file diffusion. For these two cases, we show analytically (via the propagator and Macroscopic Fluctuation Theory, respectively) that the long-term memory of initial conditions is mediated by a single static quantity: a generalized compressibility that quantifies the density fluctuations of the initial state. We thereby identify a universality class of hyperuniform initial states whose dynamical variances coincide with the quenched' cases studied previously; we also describe a continuous family of other classes among which equilibrated (or annealed') initial conditions are but one family member. We verify our predictions through extensive Monte Carlo simulations.

Description

Keywords

cond-mat.stat-mech, cond-mat.stat-mech

Journal Title

Physical Review E: Statistical, Nonlinear, and Soft Matter Physics

Conference Name

Journal ISSN

1539-3755

Volume Title

106

Publisher

American Physical Society
Sponsorship
ERC and royal society