Hybrid form of quantum theory with non-Hermitian Hamiltonians

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F23%3A00570944" target="_blank" >RIV/61389005:_____/23:00570944 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/62690094:18470/23:50020913

Výsledek na webu

<a href="https://doi.org/10.1016/j.physleta.2022.128556" target="_blank" >https://doi.org/10.1016/j.physleta.2022.128556</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.physleta.2022.128556" target="_blank" >10.1016/j.physleta.2022.128556</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Hybrid form of quantum theory with non-Hermitian Hamiltonians

Popis výsledku v původním jazyce

In Schrodinger picture the unitarity of evolution is usually guaranteed by the Hermiticity of the Hamiltonian operator 1) = 1)dagger in a conventional Hilbert space Htextbook. After a Dyson-inspired operatortransformation (OT) non-unitary preconditioning S2 : 1) -> H the simplified Hamiltonian H is, in its manifestly unphysical Hilbert space Hauxiliary, non-Hermitian. Besides its natural OT-based physical interpretation it can also be 'Hermitized' (i.e., made compatible with the unitarity) via a metric-amendment (MA) change of the Hilbert space, Hauxiliary -> Hphysical. In our present letter we propose another, third, hybrid form (HF) of the Hermitization of H in which the change involves, simultaneously, both the Hamiltonian and the metric. Formally this means that the original Dyson map is assumed factorizable, S2 = S2MS2H. A key practical advantage of the new HF approach lies in the model-dependent adaptability of such a factorization. The flexibility and possible optimality of the balance between the MA-related (i.e., metric-amending) factor S2M and the OT-related (i.e., Hamiltonian-changing) factor S2H are explicitly illustrated via an elementary two-state quantum model.

Název v anglickém jazyce

Hybrid form of quantum theory with non-Hermitian Hamiltonians

Popis výsledku anglicky

In Schrodinger picture the unitarity of evolution is usually guaranteed by the Hermiticity of the Hamiltonian operator 1) = 1)dagger in a conventional Hilbert space Htextbook. After a Dyson-inspired operatortransformation (OT) non-unitary preconditioning S2 : 1) -> H the simplified Hamiltonian H is, in its manifestly unphysical Hilbert space Hauxiliary, non-Hermitian. Besides its natural OT-based physical interpretation it can also be 'Hermitized' (i.e., made compatible with the unitarity) via a metric-amendment (MA) change of the Hilbert space, Hauxiliary -> Hphysical. In our present letter we propose another, third, hybrid form (HF) of the Hermitization of H in which the change involves, simultaneously, both the Hamiltonian and the metric. Formally this means that the original Dyson map is assumed factorizable, S2 = S2MS2H. A key practical advantage of the new HF approach lies in the model-dependent adaptability of such a factorization. The flexibility and possible optimality of the balance between the MA-related (i.e., metric-amending) factor S2M and the OT-related (i.e., Hamiltonian-changing) factor S2H are explicitly illustrated via an elementary two-state quantum model.

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

Physics Letters. A

ISSN

0375-9601

e-ISSN

1873-2429

Svazek periodika

457

Číslo periodika v rámci svazku

JAN

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

5

Strana od-do

128556

Kód UT WoS článku

000957963800002

EID výsledku v databázi Scopus

2-s2.0-85142372103