Three Alternative Model-Building Strategies Using Quasi-Hermitian Time-Dependent Observables

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F23%3A00575352" target="_blank" >RIV/61389005:_____/23:00575352 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/62690094:18470/23:50020905

Výsledek na webu

<a href="https://doi.org/10.3390/sym15081596" target="_blank" >https://doi.org/10.3390/sym15081596</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/sym15081596" target="_blank" >10.3390/sym15081596</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Three Alternative Model-Building Strategies Using Quasi-Hermitian Time-Dependent Observables

Popis výsledku v původním jazyce

In the conventional (so-called Schrodinger-picture) formulation of quantum theory the operators of observables are chosen self-adjoint and time-independent. In the recent innovation of the theory, the operators can be not only non-Hermitian but also time-dependent. The formalism (called non-Hermitian interaction-picture, NIP) requires a separate description of the evolution of the time-dependent states ? (t) (using Schrodinger-type equations) as well as of the time-dependent observables ?(j)(t), j = 1, 2, ... , K (using Heisenberg-type equations). In the unitary-evolution dynamical regime of our interest, both of the respective generators of the evolution (viz., in our notation, the Schrodingerian generator G(t) and the Heisenbergian generator S(t)) have, in general, complex spectra. Only the spectrum of their superposition remains real. Thus, only the observable superposition H(t) = G(t) + S(t) (representing the instantaneous energies) should be called Hamiltonian. In applications, nevertheless, the mathematically consistent models can be based not only on the initial knowledge of the energy operator H(t) (forming a 'dynamical' model-building strategy) but also, alternatively, on the knowledge of the Coriolis force S(t) (forming a 'kinematical' model-building strategy), or on the initial knowledge of the Schrodingerian generator G(t) (forming, for some reason, one of the most popular strategies in the literature). In our present paper, every such choice (marked as 'one', 'two' or 'three', respectively) is shown to lead to a construction recipe with a specific range of applicability.

Název v anglickém jazyce

Three Alternative Model-Building Strategies Using Quasi-Hermitian Time-Dependent Observables

Popis výsledku anglicky

In the conventional (so-called Schrodinger-picture) formulation of quantum theory the operators of observables are chosen self-adjoint and time-independent. In the recent innovation of the theory, the operators can be not only non-Hermitian but also time-dependent. The formalism (called non-Hermitian interaction-picture, NIP) requires a separate description of the evolution of the time-dependent states ? (t) (using Schrodinger-type equations) as well as of the time-dependent observables ?(j)(t), j = 1, 2, ... , K (using Heisenberg-type equations). In the unitary-evolution dynamical regime of our interest, both of the respective generators of the evolution (viz., in our notation, the Schrodingerian generator G(t) and the Heisenbergian generator S(t)) have, in general, complex spectra. Only the spectrum of their superposition remains real. Thus, only the observable superposition H(t) = G(t) + S(t) (representing the instantaneous energies) should be called Hamiltonian. In applications, nevertheless, the mathematically consistent models can be based not only on the initial knowledge of the energy operator H(t) (forming a 'dynamical' model-building strategy) but also, alternatively, on the knowledge of the Coriolis force S(t) (forming a 'kinematical' model-building strategy), or on the initial knowledge of the Schrodingerian generator G(t) (forming, for some reason, one of the most popular strategies in the literature). In our present paper, every such choice (marked as 'one', 'two' or 'three', respectively) is shown to lead to a construction recipe with a specific range of applicability.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

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

Symmetry-Basel

ISSN

2073-8994

e-ISSN

2073-8994

Svazek periodika

15

Číslo periodika v rámci svazku

8

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

13

Strana od-do

1596

Kód UT WoS článku

001056629400001

EID výsledku v databázi Scopus

2-s2.0-85168876023