Fragile PT-symmetry in a solvable model
arXiv:math-ph/0403033 · doi:10.1063/1.1803928
Abstract
One of the simplest pseudo-Hermitian models with real spectrum (viz., square-well on a real interval I of coordinates) is re-examined. A PT-symmetric complex deformation C of I is introduced and shown tractable via an innovated approach to matching conditions. The result is surprising: an arbitrarily small deformation I -> C implies a sudden collapse (i.e., the spontaneous PT-symmetry breaking) of virtually all the spectrum (i.e., up to its low-energy part).
Prepared for presentation during VI-th Meeting of Math. Physicists (Czech. Phys. Soc.), March 19 - 20, 2004, Olomouc, Czech Republic