We investigate the elementary rearrangements of energy bands in slow-fast one-parameter families of systems whose fast subsystem possesses a half-integer spin. Beginning with a simple case without any time-reversal symmetries, we analyze and compare increasingly sophisticated model Hamiltonians with these symmetries. The models are inspired by the time-reversal modification of the Berry phase setup which uses a family of quadratic spin-quadrupole Hamiltonians of Mead [Phys. Rev. Lett. 59, 161–164 (1987)] and Avron et al [Commun. Math. Phys. 124(4), 595–627 (1989)]. An explicit correspondence between the typical quantum energy level patterns in the energy band rearrangements of the finite particle systems with compact slow phase space and those of the Dirac oscillator is found in the limit of linearization near the conical degeneracy point of the semi-quantum eigenvalues.

中文翻译：

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在存在动量反转对称的情况下，角动量耦合，狄拉克振荡器和量子带重排

我们研究慢速单参数系统的快速子带具有半整数自旋的能带的基本重排。从一个没有时间反转对称性的简单案例开始，我们分析并比较了具有这些对称性的日趋完善的模型哈密顿量。这些模型的灵感源于Berry相设置的时间反转修改，该修改使用了Mead的一组二次自旋四极哈密顿量[Phys。牧师 59，161-164（1987）]和Avron等人[COMMUN。数学。物理 124（4），595–627（1989）]。在半量子特征值的圆锥简并点附近的线性化极限中，发现了具有紧凑慢相空间的有限粒子系统的能带重排中的典型量子能级模式与Dirac振荡器的典型量子能级模式之间存在明显的对应关系。