• DOI:10.1142/S0217732301005722
• Corpus ID: 14234614

Spontaneous breakdown of PT symmetry in the solvable square-well model

@article{Znojil2001SpontaneousBO,
  title={Spontaneous breakdown of PT symmetry in the solvable square-well model},
  author={Miloslav Znojil and G{\'e}za L{\'e}vai},
  journal={arXiv: High Energy Physics - Theory},
  year={2001}
}

• M. Znojil, G. Lévai
• Published 20 November 2001
• Physics
• arXiv: High Energy Physics - Theory

In many PT symmetric models with real spectra, apparently, energy levels "merge and disappear" at a point of the spontaneous PT-symmetry breaking. We argue that such an oversimplified and discontinuous physical interpretation of this mechanism as proposed, e.g., by one of us in Phys. Lett. A 285 (2001), p. 7 would be inappropriate. Using the elementary square-well model of the above reference in the strongly non-Hermitian regime we exemplify how the doublets of states with broken PT symmetry continue to exist at complex conjugate energies. In contrast to many other exactly solvable examples of such a mechanism (we listed some of them in quant-ph/0110064), our present model of symmetry breaking does not complexify all the spectrum at once. "Realistically", it rather proceeds step by step, starting from the low-lying part of the spectrum and involving more and more excited states with an increasing degree of non-Hermiticity of the underlying interaction.