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.

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

TATEO, Roberto
2009-01-01

Abstract

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.
2009
42
465302-1
465302-42
http://xxx.lanl.gov/pdf/0907.3673
CONFORMAL FIELD-THEORY, QUANTUM-MECHANICS, STOKES MULTIPLIERS, BETHE-ANSATZ,
P. Dorey; C. Dunning; A. Lishman; R. Tateo
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/71679
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