Quantum catastrophes: a case study

Abstract

The bound-state spectrum of a Hamiltonian H is assumed real in a non-empty domain D of physical values of parameters. This means that for these parameters, H may be called crypto-Hermitian, i.e., made Hermitian via an {\it ad hoc} choice of the inner product in the physical Hilbert space of quantum bound states (i.e., via an {\it ad hoc} construction of the so called metric). The name of quantum catastrophe is then assigned to the N-tuple-exceptional-point crossing, i.e., to the scenario in which we leave domain D along such a path that at the boundary of D, an N-plet of bound state energies degenerates and, subsequently, complexifies. At any fixed $N\ge 2$, this process is simulated via an N by N benchmark effective matrix Hamiltonian H. Finally, it is being assigned such a closed-form metric which is made unique via an N-extrapolation-friendliness requirement.

23 pp

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• Exceptional points and photonic catastrophe
• Admissible perturbations and false instabilities in PT-symmetric quantum systems
• Loschmidt echo and fidelity decay near an exceptional point
• Multiply Degenerate Exceptional Points and Quantum Phase Transitions
• Three solvable matrix models of a quantum catastrophe
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• Complex symmetric Hamiltonians and exceptional points of order four and five
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• Confluences of exceptional points and a systematic classification of quantum catastrophes
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• Hermitian--to--quasi-Hermitian quantum phase transitions
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