Feasibility and method of multi-step Hermitization of crypto-Hermitian quantum Hamiltonians

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F22%3A00556198" target="_blank" >RIV/61389005:_____/22:00556198 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/62690094:18470/22:50019632

Výsledek na webu

<a href="https://doi.org/10.1140/epjp/s13360-022-02567-0" target="_blank" >https://doi.org/10.1140/epjp/s13360-022-02567-0</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1140/epjp/s13360-022-02567-0" target="_blank" >10.1140/epjp/s13360-022-02567-0</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Feasibility and method of multi-step Hermitization of crypto-Hermitian quantum Hamiltonians

Popis výsledku v původním jazyce

Even the most economical conventional formulation of quantum mechanics called Schrodinger picture (SP) need not be always computationally or conceptually optimal. A Dyson-inspired remedy can sometimes be sought in a transfer of the calculations from the conventional and correct SP Hilbert space H into a 'false but friendlier' Hilbert space R. The difference (i.e., non-equivalence) between R. and H is given by a judicious simplification of the inner product. Although the Hamiltonian H itself appears non-Hermitian in R, its necessary Hermitization (mediated by a return to H) is usually feasible. If not, another eligible remedy is described in the present paper. Our basic idea lies in the introduction of a 'chained' auxiliary manipulation multiplet of inner-product spaces R-1, R-2, ..., R-N. At arbitrary N, the structure and properties of the resulting generalized SP (GSP) formulation of quantum mechanics of unitary systems (characterized by 'hiddenly Hermitian' observables) are described and discussed in detail. Nontrivial nature of the related multi-step Dyson-map composition laws and correspondences to the conventional Hermitian models are also revealed and clarified.

Název v anglickém jazyce

Feasibility and method of multi-step Hermitization of crypto-Hermitian quantum Hamiltonians

Popis výsledku anglicky

Even the most economical conventional formulation of quantum mechanics called Schrodinger picture (SP) need not be always computationally or conceptually optimal. A Dyson-inspired remedy can sometimes be sought in a transfer of the calculations from the conventional and correct SP Hilbert space H into a 'false but friendlier' Hilbert space R. The difference (i.e., non-equivalence) between R. and H is given by a judicious simplification of the inner product. Although the Hamiltonian H itself appears non-Hermitian in R, its necessary Hermitization (mediated by a return to H) is usually feasible. If not, another eligible remedy is described in the present paper. Our basic idea lies in the introduction of a 'chained' auxiliary manipulation multiplet of inner-product spaces R-1, R-2, ..., R-N. At arbitrary N, the structure and properties of the resulting generalized SP (GSP) formulation of quantum mechanics of unitary systems (characterized by 'hiddenly Hermitian' observables) are described and discussed in detail. Nontrivial nature of the related multi-step Dyson-map composition laws and correspondences to the conventional Hermitian models are also revealed and clarified.

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

2022

Kód důvěrnosti údajů

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

Název periodika

European Physical Journal Plus

ISSN

2190-5444

e-ISSN

2190-5444

Svazek periodika

137

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

15

Strana od-do

335

Kód UT WoS článku

000767933400001

EID výsledku v databázi Scopus

2-s2.0-85126458832