论文标题
零件的热力学极限
Thermodynamic limit of the Pieces' Model V2
论文作者
论文摘要
我们研究了热力学极限中费米 - 迪拉克统计中碎片模型的基态。换句话说，当$ \ frac {n} {\ frac {\vertλ\ vert} \ρ>ρ> 0 $ as as as as a as As $ \vertλ /λλ\ vert \ vert \ \ vert \ to f to ifty $。我们注意到，将有限范围的成对相互作用的假设引起了分解成碎片的组。根据子系统的凸度和非分类的假设，我们几乎完全分解了任何基态状态。此方法至少适用于包含一个或两个颗粒的组。它将每个粒子基态能量的热力学极限提高到误差$ o（ρ^{2-δ}）$，并使用$ 0 <Δ<1 $。它还为碎片的模型提供了近似的基态。
We study the ground states of the pieces' model in the Fermi-Dirac statistics in the thermodynamic limit. In other words, we consider the minimizing configurations of $ n $ interacting fermions in an interval $ Λ$ divided into pieces by a Poisson point process, when $ \frac{n}{\vert Λ\vert}\to ρ>0 $ as $ \vert Λ\vert \to \infty $. We notice that a decomposition into groups of pieces arises from the hypothesis of finite-range pairwise interaction. Under assumptions of convexity and non-degeneracy of the subsystems, we get an almost complete factorization of any ground state. This method applies at least for groups comprising one or two particles. It improves the expansion of the thermodynamic limit of the ground state energy per particle up to the error $ O(ρ^{2-δ}) $, with $ 0<δ<1 $. It also provides an approximate ground state for the pieces' model.
