title: 2 × 2 PT-symmetric matrices and their applications.
abstract: Two formulations for constructing a non-Hermitian matrix with all real eigenvalues are studied. They are called PT symmetry and pseudo-Hermiticity in the literature. Explicit 2×2 matrices of both forms are provided. They are characterized by six real parameters and are hence more general than Hermitian matrices. The equivalence of the two formulations is established. A 2×2 matrix with all real eigenvalues is PT-symmetric and pseudo-Hermitian at the same time. The application in time-dependent problems is discussed and a new geometry phase is obtained.
authors.affiliation: Department of Physics, National University of Singapore, Singapore 117542, Republic of Singapore. qhwang@nus.edu.sg
authors.forename: Qing-hai
authors.initials: QH
authors.lastname: Wang