Metastable diffusions with degenerate drifts
Copyright policy )Metastable diffusions with degenerate drifts
We study the spectrum of the semiclassical Witten Laplacian Δ f associated to a smooth function f on ℝ d . We assume that f is a confining Morse–Bott function. Under this assumption we show that Δ f admits exponentially small eigenvalues separated from the rest of the spectrum. Moreover, we establish Eyring–Kramers formula for these eigenvalues. Our approach is based on microlocal constructions of quasimodes near the critical submanifolds.
Asymptotic distributions of eigenvalues in context of PDEs, Probability (math.PR), Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory, Mathematics - Spectral Theory, Mathematics - Analysis of PDEs, Schrödinger operator, Schrödinger equation, Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics, FOS: Mathematics, spectral asymptotic, Witten Laplacian, overdamped Langevin dynamics, Spectral Theory (math.SP), Mathematics - Probability, semiclassical analysis, Analysis of PDEs (math.AP)
Asymptotic distributions of eigenvalues in context of PDEs, Probability (math.PR), Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory, Mathematics - Spectral Theory, Mathematics - Analysis of PDEs, Schrödinger operator, Schrödinger equation, Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics, FOS: Mathematics, spectral asymptotic, Witten Laplacian, overdamped Langevin dynamics, Spectral Theory (math.SP), Mathematics - Probability, semiclassical analysis, Analysis of PDEs (math.AP)
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