论文标题
费米子半经典LP估计值
Fermionic semiclassical Lp estimates
论文作者
论文摘要
我们概括了Koch，Tataru和Zworski的半古典LP估计值，在Schr {Ö} Dinger操作员的设置中，具有限制为密度矩阵的电势。这是由于捕获潜力中游离费米颗粒浓度的浓度的问题。我们的证明依赖于半经典和多体工具。作为应用程序，我们在光谱簇上提供界限。我们还通过明确的准示例讨论了一体和多体界限的最佳性。
We generalize the semiclassical Lp estimates of Koch, Tataru and Zworski in the setting of Schr{ö}dinger operators with confining potentials to density matrices. This is motivated by the problem of the concentration of free fermionic particles in a trapping potential. Our proof relies on semiclassical and many-body tools. As an application, we provide bounds on spectral clusters. We also discuss the optimality of the one-body and many-body bounds through explicit examples of quasimodes.
