On the metric operator for the imaginary cubic oscillator

P. Siegl*, D. Krejčiřík

*Corresponding author for this work

Research output: Contribution to journalArticle

73 Citations (Scopus)

Abstract

We show that the eigenvectors of the PT-symmetric imaginary cubic oscillator are complete, but do not form a Riesz basis. This results in the existence of a bounded metric operator having intrinsic singularity reflected in the inevitable unboundedness of the inverse. Moreover, the existence of nontrivial pseudospectrum is observed. In other words, there is no quantum-mechanical Hamiltonian associated with it via bounded and boundedly invertible similarity transformations. These results open new directions in physical interpretation of PT-symmetric models with intrinsically singular metric, since their properties are essentially different with respect to self-adjoint Hamiltonians, for instance, due to spectral instabilities.

Original languageEnglish
Article number121702
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Volume86
Issue number12
DOIs
Publication statusPublished - 04 Dec 2012
Externally publishedYes

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

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