PT symmetry breaking and exceptional points for a class of inhomogeneous complex potentials - High Energy Physics - TheoryReport as inadecuate




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Abstract: We study a three-parameter family of PT-symmetric Hamiltonians, related viathe ODE-IM correspondence to the Perk-Schultz models. We show that realeigenvalues merge and become complex at quadratic and cubic exceptional points,and explore the corresponding Jordon block structures by exploiting thequasi-exact solvability of a subset of the models. The mapping of the phasediagram is completed using a combination of numerical, analytical andperturbative approaches. Among other things this reveals some novel propertiesof the Bender-Dunne polynomials, and gives a new insight into a phasetransition to infinitely-many complex eigenvalues that was first observed byBender and Boettcher. A new exactly-solvable limit, the inhomogeneous complexsquare well, is also identified.



Author: Patrick Dorey, Clare Dunning, Anna Lishman, Roberto Tateo

Source: https://arxiv.org/







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