On the pseudospectrum of the harmonic oscillator with imaginary cubic potential

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F15%3A00235404" target="_blank" >RIV/68407700:21340/15:00235404 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/61389005:_____/15:00450506

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s10773-015-2530-5" target="_blank" >http://dx.doi.org/10.1007/s10773-015-2530-5</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10773-015-2530-5" target="_blank" >10.1007/s10773-015-2530-5</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On the pseudospectrum of the harmonic oscillator with imaginary cubic potential

Popis výsledku v původním jazyce

We study the Schrödinger operator with a potential given by the sum of the potentials for harmonic oscillator and imaginary cubic oscillator and we focus on its pseudospectral properties. A summary of known results about the operator and its spectrum isprovided and the importance of examining its pseudospectrum as well is emphasized. This is achieved by employing scaling techniques and treating the operator using semiclassical methods. The existence of pseudoeigenvalues very far from the spectrum is proven, and as a consequence, the spectrum of the operator is unstable with respect to small perturbations and the operator cannot be similar to a self-adjoint operator via a bounded and boundedly invertible transformation. It is shown that its eigenfunctions form a complete set in the Hilbert space of square-integrable functions; however, they do not form a Schauder basis.

Název v anglickém jazyce

On the pseudospectrum of the harmonic oscillator with imaginary cubic potential

Popis výsledku anglicky

We study the Schrödinger operator with a potential given by the sum of the potentials for harmonic oscillator and imaginary cubic oscillator and we focus on its pseudospectral properties. A summary of known results about the operator and its spectrum isprovided and the importance of examining its pseudospectrum as well is emphasized. This is achieved by employing scaling techniques and treating the operator using semiclassical methods. The existence of pseudoeigenvalues very far from the spectrum is proven, and as a consequence, the spectrum of the operator is unstable with respect to small perturbations and the operator cannot be similar to a self-adjoint operator via a bounded and boundedly invertible transformation. It is shown that its eigenfunctions form a complete set in the Hilbert space of square-integrable functions; however, they do not form a Schauder basis.

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/GA14-06818S" target="_blank" >GA14-06818S: Rigorózní metody v kvantové dynamice: geometrie a magnetická pole</a><br>

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2015

Kód důvěrnosti údajů

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

Název periodika

International Journal of Theoretical Physics

ISSN

0020-7748

e-ISSN

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Svazek periodika

54

Číslo periodika v rámci svazku

11

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

12

Strana od-do

4142-4153

Kód UT WoS článku

000362889400027

EID výsledku v databázi Scopus

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