Magnetic ring chains with vertex coupling of a preferred orientation

Quantum graphs with vertices of a preferred orientation

Motivated by a recent application of quantum graphs to model the anomalous Hall effect we discuss quantum graphs the vertices of which exhibit a preferred orientation. We describe an example of such a vertex coupling and analyze the corresponding band spectra of lattices with square and hexagonal elementary cells showing that they depend heavily on the network topology, in particular, on the degrees of the vertices involved.

具有优先取向顶点耦合的磁场中方格晶格

Magnetic square lattice with vertex coupling of a preferred orientation

本文研究磁场中方格晶格在破坏时间反演不变性的特定顶点耦合下的能谱，通过数值计算表明磁场与顶点耦合相互竞争，且高能下磁场主导并渐近恢复 Hofstadter 蝴蝶图案。

优选方向量子图的谱统计

Spectral statistics of preferred orientation quantum graphs

本研究探讨了具有优选方向顶点条件的量子图的谱统计，发现其与随机矩阵理论预测存在偏差，并通过周期轨道组合学（尤其是欧拉回路计数）提供了详细解释。

Kagome network with vertex coupling of a preferred orientation

We investigate spectral properties of periodic quantum graphs in the form of a kagome or a triangular lattice in the situation when the condition matching the wave functions at the lattice vertices is chosen of a particular form violating the time-reversal invariance. The positive spectrum consists of infinite number of bands, some of which may be flat; the negative one has at most three and two bands, respectively. The kagome lattice example shows that even in graphs with such an uncommon vertex coupling spectral universality may hold: if its edges are incommensurate, the probability that a r…

具有优先取向顶点条件的量子图特征值优化

Optimization of quantum graph eigenvalues with preferred orientation vertex conditions

本文研究顶点耦合破坏时间反演不变性的有限度量图 Laplacian 谱，在固定总边长下确定星形图基态特征值最大的构型，并为一般图的全部特征值建立上界。

Ring chains with vertex coupling of a preferred orientation

We consider a family of Schrödinger operators supported by a periodic chain of loops connected either tightly or loosely through connecting links of the length $\ell>0$ with the vertex coupling which is non-invariant with respect to the time reversal. The spectral behavior of the model illustrates that the high-energy behavior of such vertices is determined by the vertex parity. The positive spectrum of the tightly connected chain covers the entire halfline while the one of the loose chain is dominated by gaps. In addition, there is a negative spectrum consisting of an infinitely degenerate ei…