English

Should PT symmetric quantum mechanics be interpreted as nonlinear?

Quantum Physics 2015-06-26 v4

Abstract

The Feshbach-type reduction of the Hilbert space to the physically most relevant "model" subspace is suggested as a means of a formal unification of the standard quantum mechanics with its recently proposed PT symmetric modification. The resulting "effective" Hamiltonians H(eff) are always Hermitian, and the two alternative forms of their energy-dependence are interpreted as a certain dynamical nonlinearity, responsible for the repulsion and/or attraction of the levels in the Hermitian and/or PT symmetric cases, respectively. The spontaneous PT symmetry breaking is then reflected by the loss of the Hermiticity of H(eff) while the pseudo-unitary evolution law persists in the unreduced Hilbert space.

Keywords

Cite

@article{arxiv.quant-ph/0103054,
  title  = {Should PT symmetric quantum mechanics be interpreted as nonlinear?},
  author = {Miloslav Znojil},
  journal= {arXiv preprint arXiv:quant-ph/0103054},
  year   = {2015}
}

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shortened version