Quantum Strips in Higher Dimensions

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F20%3A00534047" target="_blank" >RIV/61389005:_____/20:00534047 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/68407700:21340/20:00343578

Výsledek na webu

<a href="https://doi.org/10.7153/oam-2020-14-41" target="_blank" >https://doi.org/10.7153/oam-2020-14-41</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.7153/oam-2020-14-41" target="_blank" >10.7153/oam-2020-14-41</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Quantum Strips in Higher Dimensions

Popis výsledku v původním jazyce

We consider the Dirichlet Laplacian in unbounded strips on ruled surfaces in any space dimension. We locate the essential spectrum under the condition that the strip is asymptotically flat. If the Gauss curvature of the strip equals zero, we establish the existence of discrete spectrum under the condition that the curve along which the strip is built is not a geodesic. On the other hand, if it is a geodesic and the Gauss curvature is not identically equal to zero, we prove the existence of Hardy-type inequalities. We also derive an effective operator for thin strips, which enables one to replace the spectral problem for the Laplace-Beltrami operator on the two-dimensional surface by a one-dimensional Schrodinger operator whose potential is expressed in terms of curvatures.nnIn the appendix, we establish a purely geometric fact about the existence of relatively parallel adapted frames for any curve under minimal regularity hypotheses.

Název v anglickém jazyce

Quantum Strips in Higher Dimensions

Popis výsledku anglicky

We consider the Dirichlet Laplacian in unbounded strips on ruled surfaces in any space dimension. We locate the essential spectrum under the condition that the strip is asymptotically flat. If the Gauss curvature of the strip equals zero, we establish the existence of discrete spectrum under the condition that the curve along which the strip is built is not a geodesic. On the other hand, if it is a geodesic and the Gauss curvature is not identically equal to zero, we prove the existence of Hardy-type inequalities. We also derive an effective operator for thin strips, which enables one to replace the spectral problem for the Laplace-Beltrami operator on the two-dimensional surface by a one-dimensional Schrodinger operator whose potential is expressed in terms of curvatures.nnIn the appendix, we establish a purely geometric fact about the existence of relatively parallel adapted frames for any curve under minimal regularity hypotheses.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA18-08835S" target="_blank" >GA18-08835S: Kvantová mechanika s nesamosdruženými operátory: přechod od spekter k pseudospektrům</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

Operators and Matrices

ISSN

1846-3886

e-ISSN

—

Svazek periodika

14

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

HR - Chorvatská republika

Počet stran výsledku

31

Strana od-do

635-665

Kód UT WoS článku

000576740400004

EID výsledku v databázi Scopus

2-s2.0-85096692089