多分散硬棒中的凝聚相变
Condensation Transition in Polydisperse Hard Rods
摘要：
本文研究了一个质量输运模型，其中在环上扩散的球形粒子可以随机交换体积$v$，总体积$V=\sum_{i=1}^N v_i$是固定的，$N$是粒子的总数.被称为$p$ -球的颗粒具有表现为$v_i^{1/p}$的线性尺寸，因此我们的模型表示具有可变直径$v_i^{1/p}$的多分散硬棒的气体。我们表明，我们的模型承认一个因子分解的稳态分布，它提供的尺寸分布，最大限度地减少自由能的多分散硬棒系统，固定的$N$和$V$的约束下。互补的方法（一方面明确的稳态分布的建设，另一方面密度泛函理论）完全和一贯的指定系统的行为。一个真实的空间凝聚转变所示发生的$p>1$：超过临界密度的宏观聚集体的形成和共存的临界流体相。我们的工作建立了随机质量传输方法和硬球流体的最佳多分散性之间的桥梁，在以前的文章中研究。
英文摘要：
We study a mass transport model, where spherical particles diffusing on a ring can stochastically exchange volume $v$, with the constraint of a fixed total volume $V=\sum_{i=1}^N v_i$, $N$ being the total number of particles. The particles, referred to as $p$-spheres, have a linear size that behaves as $v_i^{1/p}$ and our model thus represents a gas of polydisperse hard rods with variable diameters $v_i^{1/p}$. We show that our model admits a factorized steady state distribution which provides the size distribution that minimizes the free energy of a polydisperse hard rod system, under the constraints of fixed $N$ and $V$. Complementary approaches (explicit construction of the steady state distribution on the one hand ; density functional theory on the other hand) completely and consistently specify the behaviour of the system. A real space condensation transition is shown to take place for $p>1$: beyond a critical density a macroscopic aggregate is formed and coexists with a critical fluid phase. Our work establishes the bridge between stochastic mass transport approaches and the optimal polydispersity of hard sphere fluids studied in previous articles.
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