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Multiply degenerate exceptional points and quantum phase transitions. (English) Zbl 1329.81037

Summary: The realization of a genuine phase transition in quantum mechanics requires that at least one of the Kato’s exceptional-point parameters becomes real. A new family of finite-dimensional and time-parametrized quantum-lattice models with such a property is proposed and studied. All of them exhibit, at a real exceptional-point time \(t=0\), the Jordan-block spectral degeneracy structure of some of their observables sampled by Hamiltonian \(H(t)\) and site-position \(Q(t)\). The passes through the critical instant \(t=0\) are interpreted as schematic simulations of non-equivalent versions of the Big-Bang-like quantum catastrophes.

MSC:

81P05 General and philosophical questions in quantum theory
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
82B26 Phase transitions (general) in equilibrium statistical mechanics
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