General PT-Symmetric Matrices
Quantum Physics
2012-12-11 v1 Mathematical Physics
math.MP
Abstract
Three ways of constructing a non-Hermitian matrix with possible all real eigenvalues are discussed. They are PT symmetry, pseudo-Hermiticity, and generalized PT symmetry. Parameter counting is provided for each class. All three classes of matrices have more real parameters than a Hermitian matrix with the same dimension. The generalized PT-symmetric matrices are most general among the three. All self-adjoint matrices process a generalized PT symmetry. For a given matrix, it can be both PT-symmetric and P'-pseudo-Hermitian with respect to some P' operators. The relation between corresponding P and P' operators is established. The Jordan block structures of each class are discussed. Explicit examples in 2x2 are shown.
Cite
@article{arxiv.1212.1861,
title = {General PT-Symmetric Matrices},
author = {Jia-wen Deng and Uwe Guenther and Qing-hai Wang},
journal= {arXiv preprint arXiv:1212.1861},
year = {2012}
}
Comments
27 pages