The effective Hamiltonian in curved quantum waveguides under mild regularity assumptions
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F12%3A00384331" target="_blank" >RIV/61389005:_____/12:00384331 - isvavai.cz</a>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
The effective Hamiltonian in curved quantum waveguides under mild regularity assumptions
Original language description
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
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BE - Theoretical physics
OECD FORD branch
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Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Reviews in Mathematical Physics
ISSN
0129-055X
e-ISSN
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Volume of the periodical
24
Issue of the periodical within the volume
7
Country of publishing house
SG - SINGAPORE
Number of pages
39
Pages from-to
"1250018/1"-"1250018/39"
UT code for WoS article
000306590500005
EID of the result in the Scopus database
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