Systematics of quasi-Hermitian representations of non-Hermitian quantum models

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F23%3A00570860" target="_blank" >RIV/61389005:_____/23:00570860 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/62690094:18470/23:50020912

Výsledek na webu

<a href="https://doi.org/10.1016/j.aop.2022.169198" target="_blank" >https://doi.org/10.1016/j.aop.2022.169198</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.aop.2022.169198" target="_blank" >10.1016/j.aop.2022.169198</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Systematics of quasi-Hermitian representations of non-Hermitian quantum models

Popis výsledku v původním jazyce

In the currently quickly growing area of applications of non -Hermitian Hamiltonians H not equal H-dagger which are quasi-Hermitian (i.e., such that H-dagger Theta not equal Theta H, with a suitable inner-product metric Theta not equal I), the correct probabilistic interpretation of the model is needed. Achieved either in the Buslaev-Grecchi-inspired spirit (BGI, one factorizes Theta = Omega dagger Omega and reconstructs the conventional Her-mitian Hamiltonian, H -> gimel = Omega H Omega(-1) = gimel(dagger)) or in the much user-friendlier, Dyson-inspired spirit (DI, one eliminates the 'dif-ficult'reference to h via the quasi-Hermiticity rule, i.e., via an 'easier'reconstruction of Theta). Here, the two model-building BGI and DI recipes are identified as the two extreme special cases of a general correct-interpretation-providing strategy. We show that at any preselected integer N one may make a choice between the BGI extreme and an N-plet of the other, consistent and physical DI-type representations of the system in which a specific, partially modified Hamiltonian is constructed as quasi -Hermitian with respect to a specific, simplified inner-product metric. In applications, any one of these N+1 options may prove optimal for a given H: A schematic three-state quantum system is discussed as an illustrative example.

Název v anglickém jazyce

Systematics of quasi-Hermitian representations of non-Hermitian quantum models

Popis výsledku anglicky

In the currently quickly growing area of applications of non -Hermitian Hamiltonians H not equal H-dagger which are quasi-Hermitian (i.e., such that H-dagger Theta not equal Theta H, with a suitable inner-product metric Theta not equal I), the correct probabilistic interpretation of the model is needed. Achieved either in the Buslaev-Grecchi-inspired spirit (BGI, one factorizes Theta = Omega dagger Omega and reconstructs the conventional Her-mitian Hamiltonian, H -> gimel = Omega H Omega(-1) = gimel(dagger)) or in the much user-friendlier, Dyson-inspired spirit (DI, one eliminates the 'dif-ficult'reference to h via the quasi-Hermiticity rule, i.e., via an 'easier'reconstruction of Theta). Here, the two model-building BGI and DI recipes are identified as the two extreme special cases of a general correct-interpretation-providing strategy. We show that at any preselected integer N one may make a choice between the BGI extreme and an N-plet of the other, consistent and physical DI-type representations of the system in which a specific, partially modified Hamiltonian is constructed as quasi -Hermitian with respect to a specific, simplified inner-product metric. In applications, any one of these N+1 options may prove optimal for a given H: A schematic three-state quantum system is discussed as an illustrative example.

Druh

J_imp - Článek v periodiku v databázi Web of Science

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

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

Annals of Physics

ISSN

0003-4916

e-ISSN

1096-035X

Svazek periodika

448

Číslo periodika v rámci svazku

JAN

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

21

Strana od-do

169198

Kód UT WoS článku

000949984000001

EID výsledku v databázi Scopus

2-s2.0-85144397616