The eigenvalue and eigenvector of a non-Hermitian Hamiltonian
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.
non-Hermitian Hamiltonianknots Hermitian operatorexceptional pointKirchhoff's current lawRLC circuit
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