Semi-classical trace formulas and heat expansions
  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 Schr\"odinger 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. 
Yves Colin De Verdi\`ere (IF)
math-ph math.MP math.SP