Matrix Hamiltonians with an algebraic guarantee of unbroken PT-symmetry

Abstract

Quantum bound-state energies are assumed generated by PT-symmetric Hamiltonians H where P is, typically, parity. It is known that their spectrum only remains real and observable (i.e., in the language of physics, the PT-symmetry remains unbroken) inside a certain domain D of couplings. We show that the boundary of this domain (i.e., certain stability and observability horizon formed by the Kato's exceptional points) remains algebraic (i.e., we determine it by closed formulae) for a certain toy-model family of N-dimensional anharmonic-oscillator-related matrix Hamiltonians with dimensions between N=2 and N=11.

arXiv comment25 pp., partially presented during the 6th International Workshop on Pseudo Hermitian Hamiltonians in Quantum Physics (16th-18th of July 2007, City University, London, http://www.staff.city.ac.uk/~fring/PT/)

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• Observation of a Chiral State in a Microwave Cavity
• SUSY Quantum Mechanics with Complex Superpotentials and Real Energy Spectra

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