2004/03/17 by Miloslav Znojil · 1 citation
Mathematics · Physics and Astronomy · #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #math-ph #math.MP #msc:47B50 #msc:81Q05
paper · pdf · doi:10.1063/1.1803928
published as J. Math. Phys. 45 (2004) 4418 - 4430 · Prepared for presentation during VI-th Meeting of Math. Physicists (Czech. Phys. Soc.), March 19 - 20, 2004, Olomouc, Czech Republic
arxiv created 2004/03/17 · openalex publication_date 2004/10/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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).