经典的Jellem阶段和Laughlin阶段
The classical Jellium and the Laughlin phase
摘要：
我讨论的结果轴承上的一个新类型的变分问题，启发分数量子霍尔物理。在后者的情况下，本文回顾的主要结果可以拼写为“从Laughlin的波函数产生的独立准空穴的相位对外部势和弱长程相互作用是稳定的”。证明的主要成分是分数量子霍尔波函数和统计力学问题之间的联系，推广了2D单组分等离子体（jelvis模型）。这种系统的密度的普遍界限，创造了“不可压缩性估计”是通过对任何配置的正电荷点的屏蔽区域的建设。后一个区域是恒定的负电荷密度的补丁，其形状被优化为整个系统（点加补丁），不会在其外部产生任何电势。
英文摘要：
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.
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