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

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Cited by in corpus (12)

• The emergence, coalescence and topological properties of multiple exceptional points and their experimental realization
• Multiply Degenerate Exceptional Points and Quantum Phase Transitions
• Passage through exceptional point: Case study
• Complex symmetric Hamiltonians and exceptional points of order four and five
• Exactly solvable $\mathcal{P}\mathcal{T}$-symmetric models in two dimensions
• Hilbert space inner products for PT-symmetric Su-Schrieffer-Heeger models
• Exceptional points of infinite order give a continuous spectrum
• Bound states emerging from below the continuum in a solvable PT-symmetric discrete Schroedinger equation
• Broken Hermiticity phase transition in Bose-Hubbard model
• Displaced harmonic oscillator $V\sim \min [(x+d{)}^2,(x-d{)}^2]$ as a benchmark double-well quantum model
• Hermitian--to--quasi-Hermitian quantum phase transitions
• Quantum phase transitions mediated by clustered non-Hermitian degeneracies