Exceptional Points – Their Universal Occurrence and Their Physical Significance

Exceptional points are singularities that occur generically in the spectrum and eigenfunctions of operators (matrices) that depend on a parameter. For self-adjoint operators they always lie in the complex plane of the parameter. Owing to their association with level repulsion they feature prominently in quantum chaos. The singularities play an important role in a variety of approximation schemes. Recent experiments have confirmed the Riemann sheet structure, (square-root type for the energies and fourth root for the wave function) and the chiral character of the eigenstates.

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