2007/03/31 by Frédéric Hérau, Frederic Herau, Michael Hitrik +2
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Computer science #Eigenvalues and eigenvectors #Exponent #Fokker–Planck equation #Geometry #Limit (mathematics) #Mathematical analysis #Mathematical optimization #Mathematical physics #Mathematics #Maxima and minima #Morse code #Partial differential equation #Physics #Point (geometry) #Quantum mechanics #Saddle #Saddle point #Spectral Theory in Mathematical Physics #Statistical physics #Type (biology) #advanced mathematical theories #math-ph #math.MP #math.SP #msc:35P15 #msc:35P20 #msc:47A10 #msc:47B44 #msc:81Q20 #msc:81Q60 #msc:82C05 #msc:82C31
paper · pdf · doi:10.1007/s00023-008-0355-y
77 pages
arxiv created 2007/07/06 · openalex publication_date 2008/04/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider operators of Kramers-Fokker-Planck type in the semi-classical limit such that the exponent of the associated Maxwellian is a Morse function with two local minima and a saddle point. Under suitable additional assumptions we establish the complete asymptotics of the exponentially small splitting between the first two eigenvalues.