Quantum graphs with singular two-particle interactions
Quantum graphs with singular two-particle interactions
复制标题
具有奇异两粒子相互作用的量子图
DOI：
10.1088/1751-8113/46/4/045206
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
J. Kerner
中科院分区：
文献类型：
--
作者：
J. Bolte;J. Kerner
我们在紧致度规图上构造了具有奇异相互作用的两粒子量子模型。哈密顿算子是拉普拉斯算子的自伴实现，拉普拉斯算子作用于定义在成对边缘上的函数，使得相互作用由边界条件提供。为了找到这样的哈密尔顿封闭和半有界二次型构造，从中提取相关的自伴算子。我们提供了这样的运营商的一般特征，而且，产生某些类的例子。然后，我们考虑全同粒子和项目玻色子和费米子空间。最后，我们表明，运营商具有纯粹的离散谱和特征值分布遵循适当的外尔渐近定律。
We construct quantum models of two particles on a compact metric graph with singular two-particle interactions. The Hamiltonians are self-adjoint realizations of Laplacians acting on functions defined on pairs of edges in such a way that the interaction is provided by boundary conditions. In order to find such Hamiltonians closed and semi-bounded quadratic forms are constructed, from which the associated self-adjoint operators are extracted. We provide a general characterization of such operators and, furthermore, produce certain classes of examples. We then consider identical particles and project to the bosonic and fermionic subspaces. Finally, we show that the operators possess purely discrete spectra and that the eigenvalues are distributed following an appropriate Weyl asymptotic law.