Semi-classical trace formulas and heat expansions

Yves Colin de Verdière (1)

1 IF - Institut Fourier

in the recent paper [Journal of Physics A, 43474-0288 (2011)], B. Helffer and R. Purice compute the second term of a semi-classical trace formula for a Schrödinger operator with magnetic field. We show how to recover their formula by using the methods developped by the geometers in the seventies for the heat expansions.

Mots clés: Trace formula; Magnetic fields; Heat expansion; Synchronous gauge

Domaines: Physique mathématique [math-ph]; Théorie spectrale [math.SP]

Yves Colin de Verdière. Semi-classical trace formulas and heat expansions. Analysis & PDE, 2012, 5 (3), pp.693--703. ⟨10.2140/apde.2012.5.693⟩. ⟨hal-00578731v4⟩