We prove upper and lower bounds on the ground-state energy of the ideal two-dimensional anyon gas. Our bounds are extensive in the particle number, as for fermions, and linear in the statistics parameter $$\alpha $$α. The lower bounds extend to Lieb–Thirring inequalities for all anyons except bosons.

中文翻译：

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理想任意子的费米子行为

我们证明了理想二维任意子气体的基态能量的上限和下限。我们的边界在粒子数上是广泛的，就像费米子一样，并且在统计参数 $$\alpha $$α 中是线性的。对于除玻色子之外的所有任意子，下界都扩展到 Lieb-Thirring 不等式。