F. Hérau, M. Hitrik, J. Sjöstrand, “Supersymmetric structures for second order differential operators”, Algebra i Analiz, 2013, Volume 25, Issue 2,Pages <nobr>125

This article is cited in 4 papers

Research Papers

Supersymmetric structures for second order differential operators

F. Hérau^a, M. Hitrik^b, J. Sjöstrand^c

^a Laboratoire de Mathématiques Jean Leray, Université de Nantes, 2, rue de la Houssinière, BP 92208, 44322 Nantes Cedex 3, France, and UMR 6629 CNRS
^b Department of Mathematics, University of California, Los Angeles, CA 90095-1555, USA
^c IMB, Université de Bourgogne, 9, Av. A. Savary, BP 47870, FR-21078 Dijon C\'edex, and UMR 5584 CNRS

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.

Keywords: eigenvalue splitting, tunnelling effect, Witten–Hodge Laplacian, Kramers–Fokker–Planck operator, Schrödinger operator.

Received: 25.10.2012

Language: English