Three solvable matrix models of a quantum catastrophe

Abstract

Three classes of finite-dimensional models of quantum systems exhibiting spectral degeneracies called quantum catastrophes are described in detail. Computer-assisted symbolic manipulation techniques are shown unexpectedly efficient for the purpose.

25 pages, 2 figures

References in corpus (9)

• Making Sense of Non-Hermitian Hamiltonians
• The physics of exceptional points
• The ODE/IM Correspondence
• Three-Hilbert-Space Formulation of Quantum Mechanics
• Closed formula for the metric in the Hilbert space of a PT-symmetric model
• Interface between Hermitian and non-Hermitian Hamiltonians in a model calculation
• Scattering theory with localized non-Hermiticities
• Maximal couplings in PT-symmetric chain-models with the real spectrum of energies
• On the Role of the Normalization Factors ${\kappa }_n$ and of the Pseudo-Metric $\mathcal{P}\ne {\mathcal{P}}^{†}$ in Crypto-Hermitian Quantum Models

Cited by in corpus (2)

• Exceptional points of infinite order give a continuous spectrum
• Bound states emerging from below the continuum in a solvable PT-symmetric discrete Schroedinger equation