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Algebra i Analiz, 2013, Volume 25, Issue 2, Pages 125–154 (Mi aa1326)  

This article is cited in 3 scientific papers (total in 3 papers)

Research Papers

Supersymmetric structures for second order differential operators

F. Héraua, M. Hitrikb, J. Sjöstrandc

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.

Full text: PDF file (353 kB)
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English version:
St. Petersburg Mathematical Journal, 2014, 25:2, 241–263

Bibliographic databases:

Received: 25.10.2012
Language:

Citation: F. Hérau, M. Hitrik, J. Sjöstrand, “Supersymmetric structures for second order differential operators”, Algebra i Analiz, 25:2 (2013), 125–154; St. Petersburg Math. J., 25:2 (2014), 241–263

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. J.-F. Bony, F. Herau, L. Michel, “Tunnel effect for semiclassical random walks”, Anal. PDE, 8:2 (2015), 289–332  crossref  mathscinet  zmath  isi  scopus
    2. Michel L., “Around supersymmetry for semiclassical second order differential operators”, Proc. Amer. Math. Soc., 144:10 (2016), 4487–4500  crossref  mathscinet  zmath  isi  scopus
    3. A. Aleman, J. Viola, “On weak and strong solution operators for evolution equations coming from quadratic operators”, J. Spectr. Theory, 8:1 (2018), 33–121  crossref  mathscinet  zmath  isi  scopus
  • Алгебра и анализ St. Petersburg Mathematical Journal
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