Vol. 5, No. 3, 2012

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Semiclassical trace formulas and heat expansions

Yves Colin de Verdière

Vol. 5 (2012), No. 3, 693–703
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