Eigenvalues bifurcating from the continuum in two-dimensional potentials generating non-Hermitian gauge fields

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F23%3A50021135" target="_blank" >RIV/62690094:18470/23:50021135 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0003491623003007?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0003491623003007?via%3Dihub</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.aop.2023.169498" target="_blank" >10.1016/j.aop.2023.169498</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Eigenvalues bifurcating from the continuum in two-dimensional potentials generating non-Hermitian gauge fields

Popis výsledku v původním jazyce

It has been recently shown that complex two-dimensional (2D) potentials V-epsilon(x, y) = V(y+i epsilon eta(x)) can be used to emulate non-Hermitian matrix gauge fields in optical waveguides. Here x and y are the transverse coordinates, V(y) and eta(x) are real functions, epsilon &gt; 0 is a small parameter, and i is the imaginary unit. The real potential V(y) is required to have at least two discrete eigenvalues in the corresponding 1D Schrodinger operator. When both transverse directions are taken into account, these eigenvalues become thresholds embedded in the continuous spectrum of the 2D operator. Small nonzero e corresponds to a non-Hermitian perturbation which can result in a bifurcation of each threshold into an eigenvalue. Accurate analysis of these eigenvalues is important for understanding the behavior and stability of optical waves propagating in the artificial non-Hermitian gauge potential. Bifurcations of complex eigenvalues out of the continuum is the main object of the present study. Using recent mathematical results from the rigorous analysis of elliptic operators, we obtain simple asymptotic expansions in e that describe the behavior of bifurcating eigenvalues. The lowest threshold can bifurcate into a single eigenvalue, while every other threshold can bifurcate into a pair of complex eigenvalues. These bifurcations can be controlled by the Fourier transform of function eta(x) evaluated at certain isolated points of the reciprocal space. When the bifurcation does not occur, the continuous spectrum of 2D operator contains a quasi-bound-state which is characterized by a strongly localized central peak coupled to small-amplitude but nondecaying tails. The analysis is applied to the case examples of parabolic and double-well potentials V(y). In the latter case, the bifurcation of complex eigenvalues can be dampened if the two wells are widely separated.

Název v anglickém jazyce

Eigenvalues bifurcating from the continuum in two-dimensional potentials generating non-Hermitian gauge fields

Popis výsledku anglicky

It has been recently shown that complex two-dimensional (2D) potentials V-epsilon(x, y) = V(y+i epsilon eta(x)) can be used to emulate non-Hermitian matrix gauge fields in optical waveguides. Here x and y are the transverse coordinates, V(y) and eta(x) are real functions, epsilon &gt; 0 is a small parameter, and i is the imaginary unit. The real potential V(y) is required to have at least two discrete eigenvalues in the corresponding 1D Schrodinger operator. When both transverse directions are taken into account, these eigenvalues become thresholds embedded in the continuous spectrum of the 2D operator. Small nonzero e corresponds to a non-Hermitian perturbation which can result in a bifurcation of each threshold into an eigenvalue. Accurate analysis of these eigenvalues is important for understanding the behavior and stability of optical waves propagating in the artificial non-Hermitian gauge potential. Bifurcations of complex eigenvalues out of the continuum is the main object of the present study. Using recent mathematical results from the rigorous analysis of elliptic operators, we obtain simple asymptotic expansions in e that describe the behavior of bifurcating eigenvalues. The lowest threshold can bifurcate into a single eigenvalue, while every other threshold can bifurcate into a pair of complex eigenvalues. These bifurcations can be controlled by the Fourier transform of function eta(x) evaluated at certain isolated points of the reciprocal space. When the bifurcation does not occur, the continuous spectrum of 2D operator contains a quasi-bound-state which is characterized by a strongly localized central peak coupled to small-amplitude but nondecaying tails. The analysis is applied to the case examples of parabolic and double-well potentials V(y). In the latter case, the bifurcation of complex eigenvalues can be dampened if the two wells are widely separated.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10304 - Nuclear physics

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

Annals of Physics

ISSN

0003-4916

e-ISSN

1096-035X

Svazek periodika

459

Číslo periodika v rámci svazku

December

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

17

Strana od-do

"Article Number: 169498"

Kód UT WoS článku

001095602800001

EID výsledku v databázi Scopus

2-s2.0-85174743214