PT symmetry breaking and exceptional points for a class of inhomogeneous complex potentials

Details PT symmetry breaking and exceptional points for a class of inhomogeneous complex potentials PT symmetry breaking and exceptional points for a class of inhomogeneous complex potentials

2009-07-21

arxiv.org/abs/0907.3673v1

J.Phys.A42:465302,2009

Physics

High Energy Physics

High Energy Physics - Theory

42 pages, many figures

Scientific paper

10.1088/1751-8113/42/46/465302

We study a three-parameter family of PT-symmetric Hamiltonians, related via the ODE/IM correspondence to the Perk-Schultz models. We show that real eigenvalues merge and become complex at quadratic and cubic exceptional points, and explore the corresponding Jordon block structures by exploiting the quasi-exact solvability of a subset of the models. The mapping of the phase diagram is completed using a combination of numerical, analytical and perturbative approaches. Among other things this reveals some novel properties of the Bender-Dunne polynomials, and gives a new insight into a phase transition to infinitely-many complex eigenvalues that was first observed by Bender and Boettcher. A new exactly-solvable limit, the inhomogeneous complex square well, is also identified.

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