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Session Chair: Michel Berthier, La Rochelle University
Location:Michel Crépeau's Lecture Hall, Pôle Communication, La Rochelle University
Pôle Communication Multimédia Reseaux, La Rochelle University, 44 Avenue Albert Einstein, La Rochelle.
From Langevin dynamics to kinetic Monte Carlo: the quasi-stationary distribution approach
Ecole des Ponts ParisTech, France
We will present a mathematical framework to draw a rigorous connection between microscopic and mesoscopic models to describe the evolutions of materials at the atomistic scale: molecular dynamics, namely Langevin or overdamped Langevin dynamics, and kinetic Monte Carlo (a.k.a. Markov State Models), namely jump Markov processes with values in a discrete state space. This analysis is useful to analyze and justify numerical methods which use the jump Markov model underlying the molecular dynamics as a support to efficiently sample the state-to-state dynamics (accelerated dynamics techniques à la D. Perez and A.F. Voter). It also provides a mathematical framework to justify the use of transition state theory and the Eyring-Kramers formula to build kinetic Monte Carlo or Markov state models.
- G. Di Gesù, T. Lelièvre, D. Le Peutrec and B. Nectoux, Sharp asymptotics of the first exit point density, Annals of PDE, 5(1), 2019.
- T. Lelièvre, Mathematical foundations of Accelerated Molecular Dynamics methods, In: W. Andreoni and S. Yip (Eds), Handbook of Materials Modeling, Springer, 2018.
- T. Lelièvre, M. Ramil and J. Reygner, Quasi-stationary distribution for the Langevin process in cylindrical domains, part I: existence, uniqueness and long-time convergence, Stochastic Processes and their Applications, 144, 176-201, (2022).