Quantum star-graph analogues of PT-symmetric square wells

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F12%3A00388204" target="_blank" >RIV/61389005:_____/12:00388204 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1139/P2012-107" target="_blank" >http://dx.doi.org/10.1139/P2012-107</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1139/P2012-107" target="_blank" >10.1139/P2012-107</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Quantum star-graph analogues of PT-symmetric square wells

Popis výsledku v původním jazyce

We recall the solvable PT-symmetric quantum square well on an interval of x E (?L, L) := G ?2? (with an a-dependent non-Hermiticity given by Robin boundary conditions) and generalize it. In essence, we just replace the support interval G ?2? (reinterpreted as an equilateral two-pointed star graph with Kirchhoff matching at the vertex x = 0) with a qpointed equilateral star graph G ?q? endowed with the simplest complex-rotation-symmetric external a-dependent Robin boundary conditions. The remarkably compact form of the secular determinant is then deduced. Its analysis reveals that (i) at any integer q = 2, 3, , there exists the same q-independent and infinite subfamily of the real energies, and (ii) at any special q = 2, 6, 10, , there exists another, additional, q-dependent infinite subfamily of the real energies. In the spirit of the recently proposed dynamical construction of the Hilbert space of a quantum system, the physical bound-state interpretation of these eigenvalues is finall

Název v anglickém jazyce

Quantum star-graph analogues of PT-symmetric square wells

Popis výsledku anglicky

We recall the solvable PT-symmetric quantum square well on an interval of x E (?L, L) := G ?2? (with an a-dependent non-Hermiticity given by Robin boundary conditions) and generalize it. In essence, we just replace the support interval G ?2? (reinterpreted as an equilateral two-pointed star graph with Kirchhoff matching at the vertex x = 0) with a qpointed equilateral star graph G ?q? endowed with the simplest complex-rotation-symmetric external a-dependent Robin boundary conditions. The remarkably compact form of the secular determinant is then deduced. Its analysis reveals that (i) at any integer q = 2, 3, , there exists the same q-independent and infinite subfamily of the real energies, and (ii) at any special q = 2, 6, 10, , there exists another, additional, q-dependent infinite subfamily of the real energies. In the spirit of the recently proposed dynamical construction of the Hilbert space of a quantum system, the physical bound-state interpretation of these eigenvalues is finall

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BE - Teoretická fyzika

OECD FORD obor

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Projekt

<a href="/cs/project/GAP203%2F11%2F1433" target="_blank" >GAP203/11/1433: Kryptohermitovské pojetí kvantové teorie a jejích aplikací</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2012

Kód důvěrnosti údajů

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

Název periodika

Canadian Journal of Physics

ISSN

0008-4204

e-ISSN

—

Svazek periodika

90

Číslo periodika v rámci svazku

12

Stát vydavatele periodika

CA - Kanada

Počet stran výsledku

7

Strana od-do

1287-1293

Kód UT WoS článku

000312158000011

EID výsledku v databázi Scopus

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