Matrix Hamiltonians with an algebraic guarantee of unbroken PT-symmetry

Details Matrix Hamiltonians with an algebraic guarantee of unbroken PT-symmetry Matrix Hamiltonians with an algebraic guarantee of unbroken PT-symmetry

2008-01-02

arxiv.org/abs/0801.0359v1

J. Phys. A: Math. Theor. 41 (2008) 244027

Physics

Mathematical Physics

25 pp., partially presented during the 6th International Workshop on Pseudo Hermitian Hamiltonians in Quantum Physics (16th-18

Scientific paper

10.1088/1751-8113/41/24/244027

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.

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