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

Banerjee, Tirthankar; Jack, Robert L.; Cates, Michael E.

doi:10.48550/arxiv.2206.08739

Cited by 1 publication

(5 citation statements)

References 48 publications

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“…Our results agree with the microscopic derivations in [22,41]. Recently, the dependence of the variance of the tracer position on the initial state has been investigated in a broader class of initial states and shown to depend on the initial state only through a specific quantity, the generalized compressibility [50]. The MFT allows us to study these more general initial states and we show that…”

Section: Introductionsupporting

confidence: 88%

“…Thus, the dependence of the second cumulant on α ic follows the same pattern for a biased tracer as that found for unbiased tracers in [50].…”

Section: The Variance For a General Initial Conditionsupporting

confidence: 69%

“…In this paper, we have investigated the problem of a biased tracer in a single-file system. Thanks to a mapping to a ZRP with a biased bond at the origin, we could write exact boundary conditions at the origin within the MFT framework, solve the high density limit, retrieve at the macroscopic scale the results of microscopic calculations [22,41] and study a whole family of initial conditions, thus generalizing the results of [50] to biased tracers. We emphasize that the boundary conditions derived here are valid for general single-file systems and thus open up the MFT framework for investigating biased tracers.…”

Section: Discussionmentioning

confidence: 99%

“…Following Banerjee et al [50], we now consider more general initial conditions described by a generalized susceptibility, such that the log-probability of a small density variation in the initial ensemble is given by…”

Section: The Variance For a General Initial Conditionmentioning

confidence: 99%

“…where we have kept terms only to quadratic order in the variation. The quantity α ic defines a generalized susceptibility, and is related to the Fano factor [50]. The generalized susceptibility α ic describes the amount of fluctuations in the initial ensemble.…”

Section: The Variance For a General Initial Conditionmentioning

confidence: 99%

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Macroscopic fluctuations of a driven tracer in the symmetric exclusion process

Dandekar¹,

Mallick²

2022

J. Phys. A: Math. Theor.

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The dynamics of an asymmetric tracer in the symmetric simple exclusion process (SEP) is mapped, in the continuous scaling limit, to the local current through the origin in the zero-range process (ZRP) with a biased bond. This allows us to study the hydrodynamics of the SEP with an asymmetric tracer with a step initial condition, leading to the average displacement as a function of the bias and the densities on both sides. We then derive the cumulant generating function of the process in the high-density limit, by using the Macroscopic Fluctuation Theory and obtain agreement with the microscopic results of Poncet et al (2021). For more general initial conditions, we show that the tracer variance in the high-density limit depends only on the generalized susceptibility in the initial condition.

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Section: Introductionsupporting

confidence: 88%

“…Thus, the dependence of the second cumulant on α ic follows the same pattern for a biased tracer as that found for unbiased tracers in [50].…”

Section: The Variance For a General Initial Conditionsupporting

confidence: 69%