Anisotropy and Asymptotic Degeneracy of the Physical-Hilbert-Space Inner-Product Metrics in an Exactly Solvable Unitary Quantum Model

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F24%3A00584994" target="_blank" >RIV/61389005:_____/24:00584994 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/62690094:18470/24:50021473

Výsledek na webu

<a href="https://doi.org/10.3390/sym16030353" target="_blank" >https://doi.org/10.3390/sym16030353</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/sym16030353" target="_blank" >10.3390/sym16030353</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Anisotropy and Asymptotic Degeneracy of the Physical-Hilbert-Space Inner-Product Metrics in an Exactly Solvable Unitary Quantum Model

Popis výsledku v původním jazyce

A unitary-evolution process leading to an ultimate collapse and to a complete loss of observability alias quantum phase transition is studied. A specific solvable N-state model is considered, characterized by a non-stationary non-Hermitian Hamiltonian. Our analysis uses quantum mechanics formulated in Schrodinger picture in which, in principle, only the knowledge of a complete set of observables (i.e., operators Lambda j) enables one to guarantee the uniqueness of the related physical Hilbert space (i.e., of its inner-product metric Theta). Nevertheless, for the sake of simplicity, we only assume the knowledge of just a single input observable (viz., of the energy-representing Hamiltonian H equivalent to Lambda 1). Then, out of all of the eligible and Hamiltonian-dependent 'Hermitizing' inner-product metrics Theta=Theta(H), we pick up just the simplest possible candidate. Naturally, this slightly restricts the scope of the theory, but in our present model, such a restriction is more than compensated for by the possibility of an alternative, phenomenologically better motivated constraint by which the time-dependence of the metric is required to be smooth. This opens a new model-building freedom which, in fact, enables us to force the system to reach the collapse, i.e., a genuine quantum catastrophe as a result of the mere conventional, strictly unitary evolution.

Název v anglickém jazyce

Anisotropy and Asymptotic Degeneracy of the Physical-Hilbert-Space Inner-Product Metrics in an Exactly Solvable Unitary Quantum Model

Popis výsledku anglicky

A unitary-evolution process leading to an ultimate collapse and to a complete loss of observability alias quantum phase transition is studied. A specific solvable N-state model is considered, characterized by a non-stationary non-Hermitian Hamiltonian. Our analysis uses quantum mechanics formulated in Schrodinger picture in which, in principle, only the knowledge of a complete set of observables (i.e., operators Lambda j) enables one to guarantee the uniqueness of the related physical Hilbert space (i.e., of its inner-product metric Theta). Nevertheless, for the sake of simplicity, we only assume the knowledge of just a single input observable (viz., of the energy-representing Hamiltonian H equivalent to Lambda 1). Then, out of all of the eligible and Hamiltonian-dependent 'Hermitizing' inner-product metrics Theta=Theta(H), we pick up just the simplest possible candidate. Naturally, this slightly restricts the scope of the theory, but in our present model, such a restriction is more than compensated for by the possibility of an alternative, phenomenologically better motivated constraint by which the time-dependence of the metric is required to be smooth. This opens a new model-building freedom which, in fact, enables us to force the system to reach the collapse, i.e., a genuine quantum catastrophe as a result of the mere conventional, strictly unitary evolution.

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

2024

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

16

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

22

Strana od-do

353

Kód UT WoS článku

001192513800001

EID výsledku v databázi Scopus

2-s2.0-85189026044