The non-Hermitian Hamiltonian is constructed with the knot operators,and then the eigenvalue and corresponding eigenvector are evaluated respectively.It manifests that the eigenvalue of a non-Hermitian Hamiltonian is a complex number,and changes with the angle and the tunable parameter.The number and position of exceptional points are obtained theoretically.Moreover,the biorthogonal normalization of the right and left eigenvectors of the non-Hermitian Hamiltonian is discussed,which is different from the case in the traditional quantum mechanics.Finally,according to the Kirchhoff's current law,the non-Hermitian Hamiltonian is realized experimentally in an electric circuit with resistor,inductor and capacitor components.
关键词
非厄密哈密顿量/扭结哈密顿算子/奇异点/基尔霍夫电流定律/RLC电路
Key words
non-Hermitian Hamiltonian/knots Hermitian operator/exceptional point/Kirchhoff's current law/RLC circuit
维普
万方数据