The Montgomery model revisited

• Autorzy: B. Helffer
• Języki publikacji: EN

Abstrakty

EN

We discuss the spectral properties of the operator
$𝔥_{ℳ }(α) := -d²/dt² + (1/2 t² - α)²$
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.

Kategorie tematyczne

• 35P15: Estimation of eigenvalues, upper and lower bounds

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2010
• Tom: 118
• Numer: 2
• Strony: 391-400

Daty

wydano

2010

Twórcy

autor

B. Helffer

• Laboratoire de Mathématiques, Université Paris-Sud and CNRS, Bât. 425, F-91405 Orsay Cedex, France

Identyfikatory

DOI

10.4064/cm118-2-3