Vol. 5, No. 3, 2012
Download this article
Download this article For screen
For printing
Recent Issues

Volume 18
Issue 4, 805–1064
Issue 3, 549–803
Issue 2, 279–548
Issue 1, 1–278

Volume 17, 10 issues

Volume 16, 10 issues

Volume 15, 8 issues

Volume 14, 8 issues

Volume 13, 8 issues

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN 1948-206X (online)
ISSN 2157-5045 (print)
 
Author index
To appear
 
Other MSP journals
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