Schrodinger Equations with Logarithmic Self-Interactions: From Antilinear PT-Symmetry to the Nonlinear Coupling of Channels

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F17%3A00479625" target="_blank" >RIV/61389005:_____/17:00479625 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.3390/sym9080165" target="_blank" >http://dx.doi.org/10.3390/sym9080165</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/sym9080165" target="_blank" >10.3390/sym9080165</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Schrodinger Equations with Logarithmic Self-Interactions: From Antilinear PT-Symmetry to the Nonlinear Coupling of Channels

Popis výsledku v původním jazyce

Schrodinger equations with non-Hermitian, but PT -symmetric quantum potentials V(x) found, recently, a new field of applicability in classical optics. The potential acquired there a new physical role of an 'anomalous' refraction index. This turned attention to the nonlinear Schrodinger equations in which the interaction term becomes state-dependent, V(x) -> W(psi(x),x). Here, the state-dependence in W(psi(x),x) is assumed logarithmic, and some of the necessary mathematical assumptions, as well as some of the potential phenomenological consequences of this choice are described. Firstly, an elementary single-channel version of the nonlinear logarithmic model is outlined in which the complex self-interaction W(psi(x),x) is regularized via a deformation of the real line of x into a self-consistently constructed complex contour C. The new role played by PT -symmetry is revealed. Secondly, the regularization is sought for a multiplet of equations, coupled via the same nonlinear self-interaction coupling of channels. The resulting mathematical structures are shown to extend the existing range of physics covered by the logarithmic Schrodinger equations.

Název v anglickém jazyce

Schrodinger Equations with Logarithmic Self-Interactions: From Antilinear PT-Symmetry to the Nonlinear Coupling of Channels

Popis výsledku anglicky

Schrodinger equations with non-Hermitian, but PT -symmetric quantum potentials V(x) found, recently, a new field of applicability in classical optics. The potential acquired there a new physical role of an 'anomalous' refraction index. This turned attention to the nonlinear Schrodinger equations in which the interaction term becomes state-dependent, V(x) -> W(psi(x),x). Here, the state-dependence in W(psi(x),x) is assumed logarithmic, and some of the necessary mathematical assumptions, as well as some of the potential phenomenological consequences of this choice are described. Firstly, an elementary single-channel version of the nonlinear logarithmic model is outlined in which the complex self-interaction W(psi(x),x) is regularized via a deformation of the real line of x into a self-consistently constructed complex contour C. The new role played by PT -symmetry is revealed. Secondly, the regularization is sought for a multiplet of equations, coupled via the same nonlinear self-interaction coupling of channels. The resulting mathematical structures are shown to extend the existing range of physics covered by the logarithmic Schrodinger equations.

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

<a href="/cs/project/GA16-22945S" target="_blank" >GA16-22945S: Kvantová Wheelerova – DeWittova rovnice a její unitárně evoluční interpretace</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2017

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

—

Svazek periodika

9

Číslo periodika v rámci svazku

8

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

18

Strana od-do

—

Kód UT WoS článku

000408751100039

EID výsledku v databázi Scopus

—