A semiclassical heat trace expansion for the perturbed harmonic   oscillator
  In this paper we study a semiclassical heat trace expansion for perturbations of the harmonic oscillator, by adapting to the semiclassical setting techniques developed by Hitrik and Polterovich in [HP]. We use the expansion to obtain certain inverse spectral results. 
Victor Guillemin, Alejandro Uribe, Zuoqin Wang
math.SP