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Solvable PT-symmetric model with a tunable interspersion of non-merging
levels
Miloslav Znojil
abstract: We study the spectrum in such a PT-symmetric square well of a diameter L
where the "strength of the non-Hermiticity" is controlled by the two
parameters, viz., by an imaginary coupling ig and by the distance d of its
onset from the origin. We solve this problem and confirm that the spectrum is
discrete and real in a non-empty interval of g. Surprisingly, a specific
distinction between the bound states is found in their asymptotic
stability/instability with respect to an unlimited growth of g. In our model,
all of the low-lying levels remain asymptotically unstable at the small d and
finite L while only the stable levels survive for d near L or in the purely
imaginary well with infinite L. In between these two extremes, an unusual and
tunable, variable pattern of the interspersed "robust" and "fragile" subspectra
of the real levels is obtained.
- oai_identifier:
- oai:arXiv.org:quant-ph/0410196
- categories:
- quant-ph
- comments:
- final version: 33 pages (plus the old 8 figures of version 1)
- doi:
- 10.1063/1.1925249
- arxiv_id:
- quant-ph/0410196
- journal_ref:
- J.Math.Phys. 46 (2005) 062109
- created:
- 2004-10-25
- updated:
- 2005-04-08
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