Quasi-Hermitian Formulation of Quantum Mechanics Using Two Conjugate Schrodinger Equations

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F23%3A00574840" target="_blank" >RIV/61389005:_____/23:00574840 - isvavai.cz</a>

Alternative codes found

RIV/62690094:18470/23:50020908

Result on the web

<a href="https://doi.org/10.3390/axioms12070644" target="_blank" >https://doi.org/10.3390/axioms12070644</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/axioms12070644" target="_blank" >10.3390/axioms12070644</a>

Result language

angličtina

Original language name

Quasi-Hermitian Formulation of Quantum Mechanics Using Two Conjugate Schrodinger Equations

Original language description

To the existing list of alternative formulations of quantum mechanics, a new version of the non-Hermitian interaction picture is added. What is new is that, in contrast to the more conventional non-Hermitian model-building recipes, the primary information about the observable phenomena is provided not only by the Hamiltonian but also by an additional operator with a real spectrum (say, R(t)) representing another observable. In the language of physics, the information carried by R(t) not equal R+(t) opens the possibility of reaching the exceptional-point degeneracy of the real eigenvalues, i.e., a specific quantum phase transition. In parallel, the unitarity of the system remains guaranteed, as usual, via a time-dependent inner-product metric Theta(t). From the point of view of mathematics, the control of evolution is provided by a pair of conjugate Schrodiner equations. This opens the possibility od an innovative dyadic representation of pure states, by which the direct use of Theta(t) is made redundant. The implementation of the formalism is illustrated via a schematic cosmological toy model in which the canonical quantization leads to the necessity of working with two conjugate Wheeler-DeWitt equations. From the point of view of physics, the 'kinematical input' operator R(t) may represent either the radius of a homogeneous and isotropic expanding empty Universe or, if you wish, its Hubble radius, or the scale factor a(t) emerging in the popular Lemaitre-Friedmann-Robertson-Walker classical solutions, with the exceptional-point singularity of the spectrum of R(t) mimicking the birth of the Universe ('Big Bang') at t = 0.

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

10101 - Pure mathematics

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2023

Confidentiality

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

Name of the periodical

AXIOMS

ISSN

2075-1680

e-ISSN

2075-1680

Volume of the periodical

12

Issue of the periodical within the volume

7

Country of publishing house

CH - SWITZERLAND

Number of pages

19

Pages from-to

644

UT code for WoS article

001039141300001

EID of the result in the Scopus database

2-s2.0-85166400217