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Supersymmetric structures for second order differential operators


Authors: F. Hérau, M. Hitrik and J. Sjöstrand
Original publication: Algebra i Analiz, tom 25 (2013), nomer 2.
Journal: St. Petersburg Math. J. 25 (2014), 241-263
MSC (2010): Primary 81Q20, 81Q60, 82C22, 82C31; Secondary 35P15, 47A75, 47B44
DOI: https://doi.org/10.1090/S1061-0022-2014-01288-5
Published electronically: March 12, 2014
MathSciNet review: 3114853
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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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Additional Information

F. Hérau
Affiliation: Laboratoire de Mathématiques Jean Leray, Université de Nantes, 2, rue de la Houssinière, BP 92208, 44322 Nantes Cedex 3, France — and — UMR 6629 CNRS
Email: herau@univ-nantes.fr

M. Hitrik
Affiliation: Department of Mathematics, University of California, Los Angeles, CA 90095-1555
Email: hitrik@math.ucla.edu

J. Sjöstrand
Affiliation: IMB, Université de Bourgogne, 9, Av. A. Savary, BP 47870, FR-21078 Dijon Cédex, France — and — UMR 5584 CNRS
Email: johannes.sjostrand@u-bourgogne.fr

DOI: https://doi.org/10.1090/S1061-0022-2014-01288-5
Keywords: Eigenvalue splitting, tunnelling effect, Witten--Hodge Laplacian, Kramers--Fokker--Planck operator, Schr\"odinger operator
Received by editor(s): October 25, 2012
Published electronically: March 12, 2014
Additional Notes: Supported by the French Agence Nationale de la Recherche, NOSEVOL project, ANR 2011 BS01019 01
Dedicated: In memory of Vladimir Buslaev
Article copyright: © Copyright 2014 American Mathematical Society