Dorey, P. and Dunning, C. and Lishman, A. and Tateo, R. (2009) PT symmetry breaking and exceptional points for a class of inhomogeneous complex potentials. Journal of Physics A, 42 (46). pp. 465302-465303.
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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 Jordan 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 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.
|Subjects:||Q Science > QA Mathematics (inc Computing science)|
|Divisions:||Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Applied Mathematics|
|Depositing User:||Clare Dunning|
|Date Deposited:||29 Jun 2011 13:31|
|Last Modified:||15 Oct 2012 13:59|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/23809 (The current URI for this page, for reference purposes)|
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