Supersymmetric structures for second order differential operators

Hérau, F.; Hitrik, M.; Sjöstrand, J.

doi:10.1090/S1061-0022-2014-01288-5

Supersymmetric structures for second order differential operators
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by F. Hérau, M. Hitrik and J. Sjöstrand

St. Petersburg Math. J. 25 (2014), 241-263

DOI: https://doi.org/10.1090/S1061-0022-2014-01288-5

Published electronically: March 12, 2014

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Abstract:

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, it is shown that no smooth supersymmetric structure can exist for a suitable interaction potential, provided that the temperatures of the baths are different.

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