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Nonlinearity of perturbations in PT-symmetric quantum mechanics
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SYSNO ASEP 0509984 Document Type C - Proceedings Paper (int. conf.) R&D Document Type Conference Paper Title Nonlinearity of perturbations in PT-symmetric quantum mechanics Author(s) Znojil, Miloslav (UJF-V) RID, ORCID, SAI
Růžička, František (UJF-V) ORCIDNumber of authors 2 Article number 012120 Source Title Journal of Physics: Conference series, 1194. - Bristol : IOP, 2019 / Burdík Č. ; Navrátil O. ; Pošta S. - ISSN 1742-6588 Number of pages 8 s. Publication form Print - P Action 32nd International Colloquium on Group Theoretical Methods in Physics (Group32) Event date 08.07.2018 - 13.07.2018 VEvent location Prague Country CZ - Czech Republic Event type WRD Language eng - English Country GB - United Kingdom Keywords Group theory ; Hilbert spaces ; quantum optics Subject RIV BE - Theoretical Physics OECD category Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect) R&D Projects GA16-22945S GA ČR - Czech Science Foundation (CSF) Institutional support UJF-V - RVO:61389005 UT WOS 000537619600118 EID SCOPUS 85065556898 DOI 10.1088/1742-6596/1194/1/012120 Annotation In the so called crypto-Hermitian formulation of quantum theory (incorporating, in particular, the PT -symmetric quantum mechanics as its special case) the unitary evolution of a system is known to be described via an apparently redundant representation of the states in a triplet of Hilbert spaces. Two of them are unitarily equivalent while the auxiliary, zeroth one is unphysical but exceptionally user-friendly. The dynamical evolution equations are, naturally, solved in the friendliest space H(0). The evaluation of experimental predictions then requires a Hermitization of the observables. This yields, as its byproduct, the correct physical Hilbert space H(1). The formalism offers the conventional probabilistic interpretation due to the Dyson-proposed unitary equivalence between H(1)and a certain conventional but prohibitively complicated textbook space H(2). The key merit of the innovation lies in its enhanced flexibility opening new ways towards nonlocal or complex-interaction unitary models. The price to pay is that the ad hoc inner product in the relevant physical Hilbert space H(1) is, by construction, Hamiltonian-dependent. We show that this implies that the Rayleigh-Schrödinger perturbation theory must be used with due care. The warning is supported by an elementary sample of quantum system near its exceptional-point phase transition. In contrast to a naive expectation, the model proves stable with respect to the admissible, self-consistently specified (i.e., physical) small perturbations. Workplace Nuclear Physics Institute Contact Markéta Sommerová, sommerova@ujf.cas.cz, Tel.: 266 173 228 Year of Publishing 2020
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