发表机构
Tata Institute of Fundamental Research（塔塔基础研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究揭示活性晶体中长波长密度涨落增强的微观机制：活性异常填充声学模式，通过保守相互作用网络传递为长程应力，导致位移协方差呈q^{-3}标度。
AI 中文摘要
活性可以增强固体中超出Mermin-Wagner-Hohenberg定理所预测的平衡涨落的长波长密度涨落，但这种增强的微观起源仍不清楚。我们研究了一个二维活性布朗晶体，其纵向和横向位移协方差按$C^u_\lambda(q)\sim q^{-3}$标度，而被动对应物遵循$q^{-2}$定律。该谱预测在二维中MSD-平台发散与$L$成正比，在三维中对数发散，在四维中有限，这与Dey等人[Nat. Commun. 16, 5498 (2025)]最近报道的结果密切对应。协方差的逆给出$H^{\mathrm{cov}}_\lambda\sim |q|^3$，相应的色散$\omega_{\mathrm{cov},\lambda}\sim q^{3/2}$，而直接机械响应给出$K_{\mathrm{resp},\lambda}\sim q^2$和声学模式$\omega_{0,\lambda}\sim q$。因此，非线性色散是由协方差定义的，而非机械定义的。迁移率和积分活性力关联保持非奇异，尽管有限持久性交叉不能完全排除。微观上，纵向和横向Irving-Kirkwood相互作用应力谱按$q^{-1}$标度。横向应力-应力关联与异常位移场连接良好，表明活性异常地填充了普通声学模式，而保守相互作用网络将由此产生的涨落传递为长程应力。三维活性FCC晶体表现出相同的低$q$配对趋势。
英文摘要
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 $C^u_λ(q)\sim q^{-3}$ 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 $H^{\mathrm{cov}}_λ\sim |q|^3$ with the corresponding dispersion $ω_{\mathrm{cov},λ}\sim q^{3/2}$, whereas direct mechanical response gives $K_{\mathrm{resp},λ}\sim q^2$ and acoustic modes with $ω_{0,λ}\sim q$. 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.
