Supersymmetric structures for second order differential operators
  Necessary and sufficient conditions are obtained for a real semiclassical partial differential operator of order two to possess a supersymmetric structure. For the operator coming from a chain of oscillators, coupled to two heat baths, we show the non-existence of a smooth supersymmetric structure, for a suitable interaction potential, provided that the temperatures of the baths are different. 
Frederic Herau, Michael Hitrik, Johannes Sjoestrand
math-ph math.AP math.MP