Should PT symmetric quantum mechanics be interpreted as nonlinear?

Details Should PT symmetric quantum mechanics be interpreted as nonlinear? Should PT symmetric quantum mechanics be interpreted as nonlinear?

2001-03-12

arxiv.org/abs/quant-ph/0103054v4

J. Nonlin. Math. Phys. 9, Suppl. 2 (2002), 122 - 133

Physics

Quantum Physics

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Scientific paper

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.

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