2 × 2 PT -symmetric matrices and their applications | Zendy

Qinghai Wang | Zendy

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2 × 2 PT -symmetric matrices and their applications

Author(s) -

Qinghai Wang

Publication year - 2013

Publication title -

philosophical transactions of the royal society a mathematical physical and engineering sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.074

H-Index - 169

eISSN - 1471-2962

pISSN - 1364-503X

DOI - 10.1098/rsta.2012.0045

Subject(s) - hermitian matrix , eigenvalues and eigenvectors , mathematics , equivalence (formal languages) , matrix (chemical analysis) , symmetric matrix , pure mathematics , matrix analysis , symmetry (geometry) , hermitian function , physics , geometry , quantum mechanics , materials science , composite material

Two formulations for constructing a non-Hermitian matrix with all real eigenvalues are studied. They are calledsymmetry 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-symmetric and pseudo-Hermitian at the same time. The application in time-dependent problems is discussed and a new geometry phase is obtained.

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