Exceptional Points, Nonnormal Matrices, Hierarchy of Spin Matrices and an Eigenvalue Problem

Abstract

Exceptional points of a class of non-hermitian Hamilton operators $\hat{H}$ of the form $\hat{H}={\hat{H}}_0+i{\hat{H}}_1$ are studied, where ${\hat{H}}_0$ and ${\hat{H}}_1$ are hermitian operators. Finite dimensional Hilbert spaces are considered. The linear operators ${\hat{H}}_0$ and ${\hat{H}}_1$ are given by spin matrices for spin $s=1/2,1,3/2,\dots$. Since the linear operators studied are nonnormal, properties of such operators are described.

general improvements, references added, measure of nonnormality introduced

References in corpus (3)

• Exceptional Points of Non-hermitian Operators
• The Chirality of Exceptional Points
• Coupling of eigenvalues of complex matrices at diabolic and exceptional points

Cited by in corpus (3)

• Level attraction in a microwave optomechanical circuit
• Light transfer transitions beyond higher-order exceptional points in parity-time and anti-parity-time symmetric waveguide arrays
• Level crossing in random matrices. II Random perturbation of a random matrix