Enhanced Long-Wavelength Fluctuations and Interaction-Stress Correlations in Active Crystals
Abstract
Activity can enhance the long-wavelength density fluctuations of a solid beyond the equilibrium fluctuations predicted by the Mermin-Wagner-Hohenberg theorem, but the microscopic origin of this enhancement remains unclear. We study a two-dimensional active Brownian crystal whose longitudinal and transverse displacement covariances scale as Cuλ(q)∼ q−3 as compared to the passive counterpart with q−2 law. This spectrum predicts an MSD-plateau divergence proportional to L in two dimensions, logarithmic in three dimensions, and finite in four dimensions, in close correspondence with recent results reported in Dey et al. [Nat. Commun. 16, 5498 (2025)]. Inverse of the Covariance gives Hcovλ∼ |q|3 with the corresponding dispersion ωcov,λ∼ q3/2, whereas direct mechanical response gives Kresp,λ∼ q2 and acoustic modes with ω0,λ∼ q. The nonlinear dispersion is therefore covariance-defined rather than mechanical. The mobility and integrated active-force correlations remain non-singular, although a finite-persistence crossover cannot be ruled out completely with the existing data. Microscopically, the longitudinal and transverse Irving-Kirkwood interaction-stress spectra scale as q−1. The transverse stress-stress correlation connects well with the anomalous displacement field, indicating that activity anomalously populates ordinary acoustic modes, while the conservative interaction network transmits the resulting fluctuations as long-ranged stress. A three-dimensional active FCC crystal exhibits the same paired low-q trends.
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BibTeX
@misc{bhattacharya2026enhanced,
title = {{Enhanced Long-Wavelength Fluctuations and Interaction-Stress Correlations in Active Crystals}},
author = {Antik Bhattacharya and Smarajit Karmakar},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00634},
eprint = {2610.00634},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00634},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Enhanced Long-Wavelength Fluctuations and Interaction-Stress Correlations in Active Crystals
AU - Antik Bhattacharya
AU - Smarajit Karmakar
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00634
UR - https://arxiv.org/abs/2610.00634
AB - Activity can enhance the long-wavelength density fluctuations of a solid beyond the equilibrium fluctuations predicted by the Mermin-Wagner-Hohenberg theorem, but the microscopic origin of this enhancement remains unclear. We study a two-dimensional active Brownian crystal whose longitudinal and transverse displacement covariances scale as C^u_λ(q)∼ q^−3 as compared to the passive counterpart with q^−2 law. This spectrum predicts an MSD-plateau divergence proportional to L in two dimensions, logarithmic in three dimensions, and finite in four dimensions, in close correspondence with recent results reported in Dey et al. [Nat. Commun. 16, 5498 (2025)]. Inverse of the Covariance gives H^cov_λ∼ |q|^3 with the corresponding dispersion ω_cov,λ∼ q^3/2, whereas direct mechanical response gives K_resp,λ∼ q^2 and acoustic modes with ω_0,λ∼ q. The nonlinear dispersion is therefore covariance-defined rather than mechanical. The mobility and integrated active-force correlations remain non-singular, although a finite-persistence crossover cannot be ruled out completely with the existing data. Microscopically, the longitudinal and transverse Irving-Kirkwood interaction-stress spectra scale as q^−1. The transverse stress-stress correlation connects well with the anomalous displacement field, indicating that activity anomalously populates ordinary acoustic modes, while the conservative interaction network transmits the resulting fluctuations as long-ranged stress. A three-dimensional active FCC crystal exhibits the same paired low-q trends.
ER -