Passage through exceptional point: Case study

• URL: http://arxiv.org/abs/2003.05876v1
• Date: Thu, 12 Mar 2020 16:12:46 GMT
• Title: Passage through exceptional point: Case study
• Authors: Miloslav Znojil
• Abstract summary: It is conjectured that the exceptional-point singularity of a one-parametric quasi-Hermitian $N$ by $N$ matrix Hamiltonian $H(t)$ can play the role of a quantum phase-transition interface connecting different dynamical regimes of a unitary quantum system.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: It is conjectured that the exceptional-point (EP) singularity of a one-parametric quasi-Hermitian $N$ by $N$ matrix Hamiltonian $H(t)$ can play the role of a quantum phase-transition interface connecting different dynamical regimes of a unitary quantum system. Six realizations of the EP-mediated quantum phase transitions "of the third kind" are described in detail. Fairly realistic Bose-Hubbard (BH) and discrete anharmonic oscillator (AO) models of any matrix dimension $N$ are considered in the initial, intermediate, or final phase. In such a linear algebraic illustration of the changes of phase, all ingredients (and, first of all, all transition matrices) are constructed in closed, algebraic, non-numerical form.

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