Rearrangement of Energy Levels between Energy Super-Bands Characterized by Second Chern Class
Rearrangement of Energy Levels between Energy Super-Bands Characterized by Second Chern Class
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以陈省二级为特征的能量超能带之间的能级重排
DOI：
10.20944/preprints202111.0172.v1
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
B. Zhilinskií
中科院分区：
文献类型：
--
作者：
D. Sadovskií;B. Zhilinskií
我们将Berry几何相结构的动力学模拟推广到Avron等人的四元数模型。在我们的动力学四元数系统中，快的半整数自旋子系统与慢的两自由度子系统相互作用。该模型在1：1：2加权SO(2)对称性和自旋反转下是不变的。除了慢子系统的四个动力学变量外，还有一个形式控制参数。我们证明了与我们的模型的能量超带重排相关的最基本的定性现象包括两个能量超带之间的一个能级的重排，当形式控制参数取与半量子本征值的锥形简并有关的特殊孤立值时，这种重排就发生了。这一定性现象是由拓扑起源的，并由伴随的半量子系统的第二类陈来刻画。通过一系列算例证实了重分布能级数与第二陈数之间的对应关系。
We generalize the dynamical analog of the Berry geometric phase setup to the quaternionic model of Avron et al. In our dynamical quaternionic system, the fast half-integer spin subsystem interacts with a slow two-degrees-of-freedom subsystem. The model is invariant under the 1:1:2 weighted SO(2) symmetry and spin inversion. There is one formal control parameter in addition to four dynamical variables of the slow subsystem. We demonstrate that the most elementary qualitative phenomenon associated with the rearrangement of the energy super-bands of our model consists of the rearrangement of one energy level between two energy superbands which takes place when the formal control parameter takes the special isolated value associated with the conical degeneracy of the semi-quantum eigenvalues. This qualitative phenomenon is of the topological origin, and is characterized by the second Chern class of the associated semi-quantum system. The correspondence between the number of redistributed energy levels and the second Chern number is confirmed through a series of examples.
作为磁性晶胞的二环面上的狄拉克振荡器的体边对应
影响因子：
1.5
作者：
M.Hirasawa;M.Hirasawa;T. Iwai and B. Zhilinskii
通讯作者：
T. Iwai and B. Zhilinskii