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A toy model of PT-symmetric Quantum Mechanics, the Squire equation and UV-IR-duality

Günther, U.; Stefani, F.; Znojil, M.
Some facts about the spectrum of a PT-symmetric quantum mechanical (PTSQM) toy model with potential V(x)=Gx2(ix)ν in a box x∈[-L,L] are presented for the parameter region ν∈[-2,0]. The corresponding Hamiltonian is selfadjoint in an appropriately chosen Krein space and for ν=-1 the spectral problem maps into that of the hydrodynamic Squire equation. It is shown that in the limit L→∞ a spectral singularity occurs and that the PTSQM ⇄ Squire mapping can be interpreted as a special type of strong-coupling ⇄ weak-coupling (UV-IR) duality. Finally, the system behavior in the vicinity of a spectral triple point is sketched.
partially based on:
J. Math. Phys. 46, (2005), 063504, math-ph/0501069.
Czech. J. Phys. 55, (2005), 1099-1106, math-ph/0506021.
Keywords: PT-symmetric Quantum Mechanics, Krein space, spectral analysis, spectral triple point, UV-IR duality
  • Invited lecture (Conferences)
    6th Workshop "Operator Theory in Krein Spaces and Operator Polynomials", 14.-17.12.2006, Berlin, Germany

Permalink: https://www.hzdr.de/publications/Publ-9029
Publ.-Id: 9029