粒子在虚数周期磁场中的能带及其结构

Band spectrum and structure of a particle in an imaginary periodic magnetic field

为了验证满足一定对称性且具有周期性的非厄密哈密顿量具有实数能带,以在虚数周期磁场中运动的二维粒子为模型,在其哈密顿量满足PT赝厄密对称的情形下,运用数值方法和WKB方法计算能带并分析能带结构。结果表明:模型在此情形下有实数能带,且能带结构与哈密顿量具有PT对称的情形相同。由此再进行分析,得到了在周期场中,PT对称和PT赝厄密对称之间存在相位对应关系。

In order to verify the fact that a non-Hermitian Hamiltonian with certain symmetries anda periodicity has a real band spectrum,aplanar charged particle interacting with a perpendicular imaginary periodic magnetic field was investigated,where its Hamiltonian satisfies PT-pseudo-Hermitian symmetry.Numerical method and WKB technique were used to calculate its band spectrum and analyze band structure.Results show that the model has a real band spectrum in this case and the band structure is identical with the case of the Hamiltonian having PTsymmetry.Further discussion indicates that PTsymmetry and PT-pseudoHermitian symmetry can be generalized to a general formulation in our model.