Nonlinearity of perturbations in PT-symmetric quantum mechanics

Kód výsledku v IS VaVaI

RIV/61389005:_____/19:00509984 - isvavai.cz

Výsledek na webu

http://dx.doi.org/10.1088/1742-6596/1194/1/012120

DOI - Digital Object Identifier

10.1088/1742-6596/1194/1/012120

Jazyk výsledku

angličtina

Název v původním jazyce

Nonlinearity of perturbations in PT-symmetric quantum mechanics

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Nonlinearity of perturbations in PT-symmetric quantum mechanics

Popis výsledku anglicky

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.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10301 - Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)

Projekt

GA16-22945S: Kvantová Wheelerova – DeWittova rovnice a její unitárně evoluční interpretace

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Journal of Physics: Conference series

ISBN

—

ISSN

1742-6588

e-ISSN

—

Počet stran výsledku

8

Strana od-do

012120

Název nakladatele

IOP

Místo vydání

Bristol

Místo konání akce

Prague

Datum konání akce

8. 7. 2018

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

000537619600118