Pseudo-Hermiticity versus PT symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian

By Ali Mostafazadeh. 2001

1,211 citations recorded by the source corpus.

We introduce the notion of pseudo-Hermiticity and show that every Hamiltonian with a real spectrum is pseudo-Hermitian. We point out that all the PT-symmetric non-Hermitian Hamiltonians studied in the literature belong to the class of pseudo-Hermitian Hamiltonians, and argue that the basic structure responsible for the particular spectral properties of these Hamiltonians is their pseudo-Hermiticity. We explore the basic properties of general pseudo-Hermitian Hamiltonians, develop pseudosupersymmetric quantum mechanics, and study some concrete examples, namely the Hamiltonian of the two-component Wheeler–DeWitt equation for the FRW-models coupled to a real massive scalar field and a class of pseudo-Hermitian Hamiltonians with a real spectrum.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8762422f367d79735710854a5463aea29e466c2e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. K. Kawabata
2. Masatoshi Sato
3. Ken Shiozaki
4. Masahito Ueda
5. P. Siegl
6. Milos Tater
7. David Krejcirík
8. Joe Viola

In Statistical and Nonlinear Physics

1. P. Siegl
2. Milos Tater
3. David Krejcirík
4. Joe Viola
5. Masatoshi Sato
6. K. Kawabata
7. O. Rosas‐Ortiz
8. B. Mielnik

Citations in the corpus

• Non-Hermitian Chern Bands. (2018, neutral): “This Hamiltonian is “η-pseudo-Hermitian” [94,95] (not PT-symmetric [38,58]), namely, it satisfies η−1H†η 1⁄4 H, where η is the direct product of spatial inversion and σz:”
• Pseudo-Hermiticity versus PT-symmetry III: Equivalence of pseudo-Hermiticity and the presence of antilinear symmetries (2002, methodology): “As we point out in [2], the Hamiltonian (18) is P -pseudo-Hermitian.”
• Topological active matter (2020, background): “[210] Mostafazadeh, A.”
• Factorization: little or great algorithm? (2004, background): “Still, further studies reveal links of the pseudo-Hermitian (pseudounitary) operators with multiple areas including cosmology (see Mostafazadeh [273]).”