MATH+ CECAM Discussion Meeting on Generalized Langevin Equations
CECAMDEMMS
Organisers
The underdamped Langevin equation is a standard model in statistical mechanics and a versatile tool to sample the GibbsBoltzmann distribution, or its path integral generalization by adding appropriate friction and random forcing terms to a Hamiltonian system of equations of motion. In most implementations of the model, the friction coefficient is positionindependent and Markovian, and the random force is a Gaussian white noise.
More recently, different groups have suggested to adopt generalized Langevin equations (GLE) for a variety of purposes, such as atomistic and multiscale simulations of biomolecules,1 materials modelling,2 turbulence modelling,3 or the simulation of open quantum systems.4 In these approaches, two major variations on the Langevin theme occur: the friction becomes nonlocal or nonMarkovian, and the noise process is not a white noise process, but typically coloured or fractional noise.5 In spite of their agreedupon relevance in various applications, GLE models are much less understood with regard to their theoretical properties or their algorithmic implementation, as compared to the standard Langevin model.6
In this discussion meeting, we shall gather experts from applied mathematics, physics and chemistry to address these aspects in different contexts. We plan indepth discussion of the stateoftheart and the open issues, in particular

GLEbased Monte Carlo methods (e.g. GLE thermostats in classical and quantum molecular dynamics, stochastic gradient descent with momenta, etc.)

ergodic properties and fast convergence to equilibrium (e.g. hypocoercivity, spectral properties, semigroup theory, etc.)

Markovian approximations of the GLE (e.g. lowrank approximations of memory ker nels, GLE driven by fractional Brownian motion, etc.)

asymptotic analysis of the GLE (e.g. slowfast systems, highfriction limits, realisation of holonomic and nonholonomic constraints, etc.)
References
Carsten Hartmann (Brandenburgische Technische Universität CottbusSenftenberg)  Organiser
Felix Höfling (Freie Universität Berlin)  Organiser
Peter Koltai (Freie Universität Berlin)  Organiser