An explicitly solvable model of the spontaneous PT-symmetry breaking

Abstract

We contemplate the pair of the purely imaginary delta-function potentials on a finite interval with Dirichlet boundary conditions. The two parameter model exhibits nicely the expected quantitative features of the unavoided level crossing and of a "phase-transition" complexification of the energies. Combining analytic and numerical techniques we investigate strength- and position-dependence of its spectrum.

arXiv commentpresented in the int. conference "Pseudo-Hermitian Hamiltonians in Quantum Physics III" (Instanbul, Koc University, June 20 - 22, 2005). accepted in Czechoslovak J. Phys

References in corpus (4)

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• Solvable PT-symmetric model with a tunable interspersion of non-merging levels
• Solvability and PT-symmetry in a double-well model with point interactions
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• A model of three coupled wave guides and third order exceptional points
• Spectral singularities in PT-symmetric Bose-Einstein condensates
• Numerical calculation of the complex berry phase in non-Hermitian systems
• Differential Realization of Pseudo-Hermiticity: A quantum mechanical analog of Einstein's field equation
• Realizing PT-symmetric BEC subsystems in closed hermitian systems
• Bifurcations and exceptional points in a PT-symmetric dipolar Bose-Einstein condensate
• Supersymmetric model of a Bose-Einstein condensate in a $\mathcal{P}\mathcal{T}$-symmetric double-delta trap
• Localised nonlinear modes in the PT-symmetric double-delta well Gross-Pitaevskii equation