论文标题
古典jellium and laughlin阶段
The classical Jellium and the Laughlin phase
论文作者
论文摘要
我讨论了有关新型的变异问题的结果，灵感来自分数量子霍尔物理学。在后一种情况下，本文审查的主要结果可以拼写为“与外部电势和弱远距离相互作用相对于laughlin的波功能产生的独立准孔的阶段是稳定的”。证明的主要成分是分数量子霍尔波函数与统计力学问题之间的联系，该问题概括了2D单组分等离子体（Jellium模型）。在此类系统密度的通用界限，通过构建筛选区域的任何配置具有正电荷的点。后一个区域是恒定，负电荷密度的斑块，其形状是针对总系统（点加贴片）优化的，不会在其外部产生任何电势。
I discuss results bearing on a variational problem of a new type, inspired by fractional quantum Hall physics. In the latter context, the main result reviewed herein can be spelled as "the phase of independent quasi-holes generated from Laughlin's wave-function is stable against external potentials and weak long-range interactions". The main ingredient of the proof is a connection between fractional quantum Hall wave-functions and statistical mechanics problems that generalize the 2D one-component plasma (jellium model). Universal bounds on the density of such systems, coined "Incompressibility estimates" are obtained via the construction of screening regions for any configuration of points with positive electric charges. The latter regions are patches of constant, negative electric charge density, whose shape is optimized for the total system (points plus patch) not to generate any electric potential in its exterior.
