A complex periodic QES potential and exceptional points

We show that the complex PT -symmetric periodic potential V (x) = −(iξ sin 2x+ N)2, where ξ is real and N is a positive integer, is quasi-exactly solvable. For odd values of N ≥ 3, it may lead to exceptional points depending upon the strength of the coupling parameter ξ. The corresponding Schrödinger equation is also shown to go over to the Mathieu equation asymptotically. The limiting value of...

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O ct 2 00 7 A complex periodic QES potential and exceptional points

We show that the complex PT -symmetric periodic potential V (x) = −(iξ sin 2x+ N)2, where ξ is real and N is a positive integer, is quasi-exactly solvable. For odd values of N ≥ 3, it may lead to exceptional points depending upon the strength of the coupling parameter ξ. The corresponding Schrödinger equation is also shown to go over to the Mathieu equation asymptotically. The limiting value of...

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ar X iv : 0 71 0 . 18 02 v 2 [ qu an t - ph ] 1 2 N ov 2 00 7 A complex periodic QES potential and exceptional points

We show that the complex PT -symmetric periodic potential V (x) = −(iξ sin 2x+ N)2, where ξ is real and N is a positive integer, is quasi-exactly solvable. For odd values of N ≥ 3, it may lead to exceptional points depending upon the strength of the coupling parameter ξ. The corresponding Schrödinger equation is also shown to go over to the Mathieu equation asymptotically. The limiting value of...

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Information Geometry of Complex Hamiltonians and Exceptional Points

Information geometry provides a tool to systematically investigate the parameter sensitivity of the state of a system. If a physical system is described by a linear combination of eigenstates of a complex (that is, non-Hermitian) Hamiltonian, then there can be phase transitions where dynamical properties of the system change abruptly. In the vicinities of the transition points, the state of the...

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Exceptional points in atomic spectra.

We report the existence of exceptional points for the hydrogen atom in crossed magnetic and electric fields in numerical calculations. The resonances of the system are investigated and it is shown how exceptional points can be found by exploiting characteristic properties of the degeneracies, which are branch point singularities. A possibility for the observation of exceptional points in an exp...

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A complex periodic QES potential and exceptional points

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