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- W2775883470 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 non-trivial 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." @default.
- W2775883470 created "2018-01-05" @default.
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- W2775883470 date "2012-08-09" @default.
- W2775883470 modified "2023-09-27" @default.
- W2775883470 title "Metric operator for the imaginary cubic oscillator does not exist" @default.
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