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

Result code in 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>

Alternative codes found

RIV/62690094:18470/24:50021473

Result on the web

<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>

Result language

angličtina

Original language name

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

Original language description

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.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10301 - Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2024

Confidentiality

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

Name of the periodical

Symmetry-Basel

ISSN

2073-8994

e-ISSN

2073-8994

Volume of the periodical

16

Issue of the periodical within the volume

3

Country of publishing house

CH - SWITZERLAND

Number of pages

22

Pages from-to

353

UT code for WoS article

001192513800001

EID of the result in the Scopus database

2-s2.0-85189026044