The Effective Hamiltonian in Curved Quantum Waveguides and When It Does Not Work
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F13%3A00210411" target="_blank" >RIV/68407700:21340/13:00210411 - isvavai.cz</a>
Result on the web
—
DOI - Digital Object Identifier
—
Alternative languages
Result language
angličtina
Original language name
The Effective Hamiltonian in Curved Quantum Waveguides and When It Does Not Work
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
—
Czech description
—
Classification
Type
D - Article in proceedings
CEP classification
BE - Theoretical physics
OECD FORD branch
—
Result continuities
Project
<a href="/en/project/LC06002" target="_blank" >LC06002: Doppler Institute for Mathematical Physics and Applied Mathematics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Microlocal Methods in Mathematical Physics and Global Analysis
ISBN
978-3-0348-0465-3
ISSN
—
e-ISSN
—
Number of pages
4
Pages from-to
29-32
Publisher name
Birkhäuser Verlag
Place of publication
Basel
Event location
Tübingen
Event date
Jun 14, 2012
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
—