Semiclassical trace formulas and heat expansions

Yves de Verdière

doi:10.2140/apde.2012.5.693

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Home > Journals > Anal. PDE > Volume 5 > Issue 3 > Article

2012 Semiclassical trace formulas and heat expansions

Yves de Verdière

Anal. PDE 5(3): 693-703 (2012). DOI: 10.2140/apde.2012.5.693

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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.