The Montgomery model revisited
Colloquium Mathematicae (2010)
- Volume: 118, Issue: 2, page 391-400
- ISSN: 0010-1354
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topB. Helffer. "The Montgomery model revisited." Colloquium Mathematicae 118.2 (2010): 391-400. <http://eudml.org/doc/286405>.
@article{B2010,
abstract = {We discuss the spectral properties of the operator
$_\{ℳ \}(α) := -d²/dt² + (1/2 t² - α)²$
on the line. We first briefly describe how this operator appears in various problems in the analysis of operators on nilpotent Lie groups, in the spectral properties of a Schrödinger operator with magnetic field and in superconductivity. We then give a new proof that the minimum over α of the groundstate energy is attained at a unique point and also prove that the minimum is non-degenerate. Our study can also be seen as a refinement for a specific nilpotent group of a general analysis proposed by J. Dziubański, A. Hulanicki and J. Jenkins.},
author = {B. Helffer},
journal = {Colloquium Mathematicae},
keywords = {Montgomery operator; harmonic oscillator; spectral theory; Schrodinger operator with magnetic fields; semi-classical analysis},
language = {eng},
number = {2},
pages = {391-400},
title = {The Montgomery model revisited},
url = {http://eudml.org/doc/286405},
volume = {118},
year = {2010},
}
TY - JOUR
AU - B. Helffer
TI - The Montgomery model revisited
JO - Colloquium Mathematicae
PY - 2010
VL - 118
IS - 2
SP - 391
EP - 400
AB - We discuss the spectral properties of the operator
$_{ℳ }(α) := -d²/dt² + (1/2 t² - α)²$
on the line. We first briefly describe how this operator appears in various problems in the analysis of operators on nilpotent Lie groups, in the spectral properties of a Schrödinger operator with magnetic field and in superconductivity. We then give a new proof that the minimum over α of the groundstate energy is attained at a unique point and also prove that the minimum is non-degenerate. Our study can also be seen as a refinement for a specific nilpotent group of a general analysis proposed by J. Dziubański, A. Hulanicki and J. Jenkins.
LA - eng
KW - Montgomery operator; harmonic oscillator; spectral theory; Schrodinger operator with magnetic fields; semi-classical analysis
UR - http://eudml.org/doc/286405
ER -
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