Repartition of the Quasi-stationary Distribution and First Exit Point Density for a Double-Well Potential

DOI10.1137/19M1246432zbMath1430.35175arXiv1902.06304MaRDI QIDQ5215743

Dorian Le Peutrec, Boris Nectoux

Publication date: 13 February 2020

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.06304

zbMATH Keywords

metastabilityquasi-stationary distributionsemiclassical analysistunneling effectdouble-welloverdamped Langevin process

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Diffusion processes (60J60) General theory of partial differential operators (47F05) Schrödinger operator, Schrödinger equation (35J10) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) PDEs in connection with statistical mechanics (35Q82)

Related Items (5)

The exit from a metastable state: concentration of the exit point distribution on the low energy saddle points. I ⋮ Non-reversible metastable diffusions with Gibbs invariant measure. II: Markov chain convergence ⋮ Asymptotic analysis of mean exit time for dynamical systems with a single well potential ⋮ Mean exit time for the overdamped Langevin process: the case with critical points on the boundary ⋮ Small eigenvalues of the Witten Laplacian with Dirichlet boundary conditions: the case with critical points on the boundary

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Eyring-Kramers law for Markovian jump processes with symmetries
• On the convergence of diffusion processes conditioned to remain in a bounded region for large time to limiting positive recurrent diffusion processes
• Killed diffusions and their conditioning
• Semi-classical analysis for the Schrödinger operator and applications
• Metastability in reversible diffusion processes. I: Sharp asymptotics for capacities and exit times
• Metastability in reversible diffusion processes. II: Precise asymptotics for small eigenvalues
• Hodge decomposition. A method for solving boundary value problems
• About small eigenvalues of the Witten Laplacian
• Sharp asymptotics of the first exit point density
• A mathematical formalization of the parallel replica dynamics
• Exponential convergence to quasi-stationary distribution for absorbed one-dimensional diffusions with killing
• Multiple wells in the semi-classical limit I
• Multiple Wells in the Semi-Classical Limit III - Interaction Through Non-Resonant Wells
• Mathematical Analysis of Temperature Accelerated Dynamics
• Partial differential equations and stochastic methods in molecular dynamics

This page was built for publication: Repartition of the Quasi-stationary Distribution and First Exit Point Density for a Double-Well Potential