Around supersymmetry for semiclassical second order differential operators

Abstract

Let $P(h),h\in ]0,1]$ be a semiclassical scalar differential operator of order $2$. The existence of a supersymmetric structure given by a matrix $G(x;h)$ was exhibited in \cite{HeHiSj13} under rather general assumptions. In this note we give a sufficient condition on its coefficient so that the matrix $G(x;h)$ enjoys some nice estimates with respect to the semiclassical parameter.

References in corpus (1)

• Tunnel effect for Kramers-Fokker-Planck type operators