Passage through exceptional point: case study

0524156 - ÚJF 2021 RIV GB eng J - Journal Article
Znojil, Miloslav
Passage through exceptional point: case study.
Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences. Roč. 476, č. 2236 (2020), č. článku 20190831. ISSN 1364-5021. E-ISSN 1471-2946
Institutional support: RVO:61389005
Keywords : quasi-Hermitian quantum Hemiltonians * non-Hermitian degeneracies * transition matrices * phase transitions * closed-form toy models
OECD category: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Impact factor: 2.704, year: 2020
Method of publishing: Open access
https://doi.org/10.1098/rspa.2019.0831

The description of unitary evolution using non-Hermitian but 'hermitizable' Hamiltonians H is feasible via an ad hoc metric Theta=Theta (H) and a (non-unique) amendment psi(1)|psi(2)->psi(1)|Theta |psi(2) of the inner product in Hilbert space. Via a proper fine-tuning of Theta (H) this opens the possibility of reaching the boundaries of stability (i.e. exceptional points) in many quantum systems sampled here by the fairly realistic Bose-Hubbard (BH) and discrete anharmonic oscillator (AO) models. In such a setting, it is conjectured that the EP singularity can play the role of a quantum phase-transition interface between different dynamical regimes. Three alternative 'AO - BH' implementations of such an EP-mediated dynamical transmutation scenario are proposed and shown, at an arbitrary finite Hilbert-space dimension N, exact and non-numerical.
Permanent Link: http://hdl.handle.net/11104/0308519