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

Kód výsledku v 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>

Nalezeny alternativní kódy

RIV/62690094:18470/23:50020908

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

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

AXIOMS

ISSN

2075-1680

e-ISSN

2075-1680

Svazek periodika

12

Číslo periodika v rámci svazku

7

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

19

Strana od-do

644

Kód UT WoS článku

001039141300001

EID výsledku v databázi Scopus

2-s2.0-85166400217