论文标题
保守的甘露砂岩中的动态相关性
Dynamic correlations in the conserved Manna sandpile
论文作者
论文摘要
我们研究一维保守的甘露砂岩中电流和质量以及相关功率光谱的动态相关性。我们表明，在热力学限制下，累积债券电流到时间$ t $的差异为$ t^{1/2-μ} $增长为$ t^{1/2-μ} $，指数$μ\ ge 0 $根据所考虑的密度制度，并且取决于所考虑的密度，同样是电流和质量的低频$ f $ $ f $ f $ f $ f^$ f^$ f^{1/2} {1/2} {1/2} $ f^{ - 3/2+μ} $；我们的理论预测，毫无疑问，$μ= 0 $，接近临界值，$μ=（β+1）/2ν_ {\ perp} z> 0 $，$β$，$β$，$ be，$ν_ {\ perp} $，$ z $分别是订单 - 参数，是订单 - 参数，correlation-last-length，correlation-last-Length，correlation-Length和Dynamic and correlation-Length和Dynamigic and corleration-Legth and Dynamigic and corleration-Length and DynamiC and corleLation-Length and。临界点接近波动的异常抑制表示“动态超均匀性”，其特征是一组波动关系，其中当前，质量和标记的粒子位移波动被证明与密度依赖性活性（或它的导数）具有精确的定量关系。特别是，关系，$ {\ mathcal {d}} _ s（\barρ）= a（\barρ） / \barρ$，在自扩散系数$ {\ MATHCAL {d MATHCAL {d}}} _ s（\barρ）$，活动$ a（\barρ）$和dentival $barρ$以前物理。 J. B \ textbf {72}，441（2009）]，几乎关键的是，甘露砂岩中的自扩散系数与活动具有相同的缩放缩放行为。
We study dynamic correlations for current and mass, as well as the associated power spectra, in the one-dimensional conserved Manna sandpile. We show that, in the thermodynamic limit, the variance of cumulative bond current up to time $T$ grows subdiffusively as $T^{1/2-μ}$ with the exponent $μ\ge 0$ depending on the density regimes considered and, likewise, the power spectra of current and mass at low frequency $f$ varies as $f^{1/2+μ}$ and $f^{-3/2+μ}$, respectively; our theory predicts that, far from criticality, $μ= 0$ and, near criticality, $μ= (β+1)/2 ν_{\perp} z > 0$ with $β$, $ν_{\perp}$ and $z$ being the order-parameter, correlation-length and dynamic exponents, respectively. The anomalous suppression of fluctuations near criticality signifies a "dynamic hyperuniformity", characterized by a set of fluctuation relations, in which current, mass and tagged-particle displacement fluctuations are shown to have a precise quantitative relationship with the density-dependent activity (or, it's derivative). In particular, the relation, ${\mathcal{D}}_s(\barρ) = a(\barρ) / \barρ$, between the self-diffusion coefficient ${\mathcal{D}}_s(\barρ)$, activity $a(\barρ)$ and density $\barρ$ explains a previous simulation observation [Eur. Phys. J. B \textbf{72}, 441 (2009)] that, near criticality, the self-diffusion coefficient in the Manna sandpile has the same scaling behavior as the activity.
