The effective Hamiltonian in curved quantum waveguides under mild regularity assuptions

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F12%3A00196871" target="_blank" >RIV/68407700:21340/12:00196871 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1142/S0129055X12500183" target="_blank" >http://dx.doi.org/10.1142/S0129055X12500183</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1142/S0129055X12500183" target="_blank" >10.1142/S0129055X12500183</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The effective Hamiltonian in curved quantum waveguides under mild regularity assuptions

Popis výsledku v původním jazyce

The Dirichlet Laplacian in a curved three-dimensional tube built along a spatial (bounded or unbounded) curve is investigated in the limit when the uniform cross-section of the tube diminishes. Both deformations due to bending and twisting of the tube are considered. We show that the Laplacian converges in a norm-resolvent sense to the well-known one-dimensional Schrödinger operator whose potential is expressed in terms of the curvature of the reference curve, the twisting angle and a constant measuringthe asymmetry of the cross-section. Contrary to previous results, we allow the reference curves to have non-continuous and possibly vanishing curvature. For such curves, the distinguished Frenet frame standardly used to define the tube need not exist and, moreover, the known approaches to prove the result for unbounded tubes do not work. To establish the norm-resolvent convergence under the minimal regularity assumptions, we use an alternative frame defined by a parallel transport along

Název v anglickém jazyce

The effective Hamiltonian in curved quantum waveguides under mild regularity assuptions

Popis výsledku anglicky

The Dirichlet Laplacian in a curved three-dimensional tube built along a spatial (bounded or unbounded) curve is investigated in the limit when the uniform cross-section of the tube diminishes. Both deformations due to bending and twisting of the tube are considered. We show that the Laplacian converges in a norm-resolvent sense to the well-known one-dimensional Schrödinger operator whose potential is expressed in terms of the curvature of the reference curve, the twisting angle and a constant measuringthe asymmetry of the cross-section. Contrary to previous results, we allow the reference curves to have non-continuous and possibly vanishing curvature. For such curves, the distinguished Frenet frame standardly used to define the tube need not exist and, moreover, the known approaches to prove the result for unbounded tubes do not work. To establish the norm-resolvent convergence under the minimal regularity assumptions, we use an alternative frame defined by a parallel transport along

Druh

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

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2012

Kód důvěrnosti údajů

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

Název periodika

Reviews in Mathematical Physics

ISSN

0129-055X

e-ISSN

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Svazek periodika

24

Číslo periodika v rámci svazku

07

Stát vydavatele periodika

SG - Singapurská republika

Počet stran výsledku

39

Strana od-do

"1250018-1"-"1250018-39"

Kód UT WoS článku

000306590500005

EID výsledku v databázi Scopus

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