Semiclassical trace formulas and heat expansions

de Verdière, Yves

doi:10.2140/apde.2012.5.693

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Semiclassical trace formulas and heat expansions

Yves Colin de Verdière

Vol. 5 (2012), No. 3, 693–703

DOI: 10.2140/apde.2012.5.693

Abstract

In a recent paper (J. Phys. A 43:47 (2011), 474028), B. Helffer and R. Purice compute the second term of a semiclassical trace formula for a Schrödinger operator with magnetic field. We show how to recover their formula by using the methods developed by Riemannian geometers in the seventies for heat expansions.

Keywords

trace formula, magnetic fields, heat expansion, synchronous gauge

Mathematical Subject Classification 2010

Primary: 35P20, 35S05, 58J35

Milestones

Received: 18 April 2011

Revised: 11 June 2011

Accepted: 11 July 2011

Published: 15 October 2012

Authors

Yves Colin de Verdière
Unité mixte de recherche CNRS-UJF 5582 Institut Fourier BP 74, 38402-Saint Martin d’Hères Cedex France

Vol. 5, No. 3, 2012