Remote Access St. Petersburg Mathematical Journal

St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



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
Published electronically: March 12, 2014
MathSciNet review: 3114853
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in St. Petersburg Mathematical Journal with MSC (2010): 81Q20, 81Q60, 82C22, 82C31, 35P15, 47A75, 47B44

Retrieve articles in all journals with MSC (2010): 81Q20, 81Q60, 82C22, 82C31, 35P15, 47A75, 47B44

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

M. Hitrik
Affiliation: Department of Mathematics, University of California, Los Angeles, CA 90095-1555

J. Sjöstrand
Affiliation: IMB, Université de Bourgogne, 9, Av. A. Savary, BP 47870, FR-21078 Dijon Cédex, France — and — UMR 5584 CNRS

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

American Mathematical Society