Fluxes, Laplacians, and Kasteleyn’s theorem
Fluxes, Laplacians, and Kasteleyn’s theorem
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DOI：
10.1215/s0012-7094-93-07114-1
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发表时间：
1992-09
影响因子：
2.5
通讯作者：
E. Lieb;M. Loss
中科院分区：
文献类型：
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作者：
E. Lieb;M. Loss
这篇论文的起源是试图理解凝聚态物理学中的一个问题，这个问题与电子相关性、超导性和电磁场相互作用有关。几年前提出的基本思想是，当电子密度不小时，磁场可以降低电子的能量。对拉普拉斯算子的特征值作了一些非常具体和有趣的数学推导，本文给出了其中一些的证明。此外，这些命题导致了关于拉普拉斯行列式的额外的自然命题，我们都在这里提出并证明。目前还不清楚这些行列式定理是否有物理应用，但可以想象，在量子场论的背景下，它们可能有。这里给出的一些结果，但不是全部，在[LE]中早些时候宣布。
The genesis of this paper was an attempt to understand a problem in condensed matter physics related to questions about electron correlations, superconductivity, and electron-magnetic field interactions. The basic idea, which was proposed a few years ago, is that a magnetic field can lower the energy of electrons when the electron density is not small. Certain very specific and very interesting mathematical conjectures about eigenvalues of the Laplacian were made, and the present paper contains a proof of some of them. Furthermore, those conjectures lead to additional natural conjectures about determinants of Laplacians which we both present and prove here. It is not clear whether these determinantal theorems have physical applications but they might, conceivably in the context of quantum field theory. Some, but not all, of the results given here were announced earlier in [LE].