Universal scale-free decay of tracer-bath correlations in $d$-dimensional interacting particle systems

TL;DR

This paper analytically derives universal power-law decay profiles for tracer-bath correlations in interacting particle systems across dimensions, revealing that these correlations depend only on spatial dimension and are robust across models.

Contribution

It provides the first analytical expressions for tracer-bath correlations in $d$-dimensional systems, uncovering universal decay features dependent solely on dimensionality.

Findings

Correlation profiles exhibit power-law tails with exponents depending on dimension.

Universal decay behavior is confirmed through numerical simulations.

Results apply to both hard-core and soft-core interaction models.

Abstract

Quantifying the correlations between the position of a tagged tracer and the density of surrounding bath particles is crucial for understanding tracer diffusion in interacting particle systems, and for characterizing the response properties of the bath. We address this problem analytically for both hard-core and soft-core interactions, using minimal yet paradigmatic models in $d$ spatial dimensions. In both cases, we derive analytical expressions for the spatial correlation profiles in the reference frame of the tracer. We reveal unexpected universal features in their large-distance behavior, characterized by power-law tails with exponents that depend solely on the spatial dimensionality of the system. Beyond these simple models, we demonstrate the robustness of our results across different regimes using particle-based numerical simulations.