0000000000281896

AUTHOR

Frédéric Hérau

showing 2 related works from this author

Supersymmetric structures for second order differential operators

2012

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, we show the non-existence of a smooth supersymmetric structure, for a suitable interaction potential, provided that the temperatures of the baths are different.

Algebra and Number Theory35P15 47A75 47B44 81Q20 81Q60 82C22 82C31Applied MathematicsFOS: Physical sciencesMathematical Physics (math-ph)Differential operatorTunnelling effectTheoretical physicsMathematics - Analysis of PDEsOrder (business)FOS: MathematicsMathematical PhysicsAnalysisMathematicsAnalysis of PDEs (math.AP)
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Tunnel effect and symmetries for Kramers–Fokker–Planck type operators

2011

AbstractWe study operators of Kramers–Fokker–Planck type in the semiclassical limit, assuming that the exponent of the associated Maxwellian is a Morse function with a finite number n0 of local minima. Under suitable additional assumptions, we show that the first n0 eigenvalues are real and exponentially small, and establish the complete semiclassical asymptotics for these eigenvalues.

Maxima and minimaComputer Science::Information RetrievalGeneral MathematicsExponentSemiclassical physicsFokker–Planck equationLimit (mathematics)Finite setEigenvalues and eigenvectorsMathematicsMorse theoryMathematical physicsJournal of the Institute of Mathematics of Jussieu
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