论文标题
凝结过渡中的有限尺寸定位方案
Finite-size localization scenarios in condensation transitions
论文作者
论文摘要
我们考虑了全球保守数量的凝结现象$ h = \ sum_ {i = 1}^nε_i$分布在$ n $站点上，当密度$ h = h/n $超过关键密度$ h_c $时发生。我们从数值上研究参与率的依赖性$ y_2 = \langleε_i^2 \ rangle/（nh^2）$对系统的$ n $以及控制参数$δ=（h-h_c）$，用于各种模型的控制参数$δ=（h-h_c）$，用于各种模型：（i）〜具有两个模型的模型，源自iNvive varrive vastive the divived varrive sheveartive。 （ii）〜零范围过程类的连续版本，用于定义分解稳态的函数$ f（ε）$的不同形式。我们的结果表明，有限$ n $并接近过渡点可能会出现各种本地化方案。这些场景的特征是在与$ n $绘制的绘制和指数$γ\ geq 2 $时，通过关系$ n^*\simeqΔ^^Δ^{ - γ{ - γ} $定义的指数$γ\ geq 2 $，其中$ n^*$从$ n \ n $ n $ n $ n \ y y_ $ n^2 $ n^2 $，区域（$ n \ gg n^*$，$ y_2 $大约是恒定的）。我们最终将结果与通过单位边缘分布获得的冷凝物的结构进行了比较。
We consider the phenomenon of condensation of a globally conserved quantity $H=\sum_{i=1}^N ε_i$ distributed on $N$ sites, occurring when the density $h= H/N$ exceeds a critical density $h_c$. We numerically study the dependence of the participation ratio $Y_2=\langle ε_i^2\rangle/(Nh^2)$ on the size $N$ of the system and on the control parameter $δ= (h-h_c)$, for various models: (i)~a model with two conservation laws, derived from the Discrete NonLinear Schrödinger equation; (ii)~the continuous version of the Zero Range Process class, for different forms of the function $f(ε)$ defining the factorized steady state. Our results show that various localization scenarios may appear for finite $N$ and close to the transition point. These scenarios are characterized by the presence or the absence of a minimum of $Y_2$ when plotted against $N$ and by an exponent $γ\geq 2$ defined through the relation $N^* \simeq δ^{-γ}$, where $N^*$ separates the delocalized region ($N\ll N^*$, $Y_2$ vanishes with increasing $N$) from the localized region ($N\gg N^*$, $Y_2$ is approximately constant). We finally compare our results with the structure of the condensate obtained through the single-site marginal distribution.
