Anti-PT transformations and complex non-Hermitian PT-symmetric superpartners

Koohrokhi T., KARTAL S., Mohammadi A.

Annals of Physics, cilt.459, 2023 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 459
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1016/j.aop.2023.169490
  • Dergi Adı: Annals of Physics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Chemical Abstracts Core, INSPEC, zbMATH
  • Anahtar Kelimeler: Anti-[Formula presented] transformations, Complex superpotential, [Formula presented] conjugation, [Formula presented]-inner product, [Formula presented]-symmetry
  • İstanbul Üniversitesi Adresli: Evet

Özet

We propose a new algebraic formalism for constructing complex non-Hermitian PT-symmetric superpartners by extending a conventional shape-invariant superpotential into the complex domain. The resulting potential is an unbroken super- and parity-time (PT)-symmetric shape-invariant potential with real energy eigenvalues, maintaining this property for all parameter values. In order to restore the probabilistic interpretation within a true quantum theory, a new inner product called the CPT-inner product is defined in PT-symmetric quantum mechanics, replacing the Dirac Hermitian inner product. In this work, we propose a new version of the inner product called the anti-PT (APT)-inner product, 〈A|B〉≡|A〉APT.|B〉, which replaces the previous versions without any additional considerations. This PT-supersymmetric quantum mechanics framework also allows for the unification of various areas of physics, including classical optics and quantum mechanics. To validate the theory, we present exact solutions for optical waveguides and the quantum tunneling probability, demonstrating excellent agreement with experimental data for the probability of crossing the potential barrier in the 3H(d,n)4He reaction.