Monte Carlo sampling of gluons by molecular dynamics

• Applicant: Professor Dr. Michael Günther
• Subject Area: Mathematics ; Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 451886959

This project will improve the Monte Carlo sampling of gauge fields including the quark effects with new mathematical insight into dynamics on Lie-group manifolds. Nested Hessian-free force-gradient schemes exploit the multirate potential within different activity levels of actions. These schemes will be tuned to the by then newly generated ensembles by projects P1 and P2 with respect to an optimal ratio between stability and efficiency. Integration schemes with Fourier acceleration will be studied, which require implicit time integration. The project develops hierarchical splitting methods including adapted Hessian-free force-gradient and nested time integration schemes. Together with the PIs of project P4, also structure-preserving nonlinear and linear system solvers will be derived to reduce the computational costs for implicit time integration schemes, i.e., time-reversibility and symplecticity is preserved for all iterates, and not only at convergence. When simulating lattice QCD at small quark masses at or close to the physical point the stability of the integrator is crucial and can be guaranteed by implicit integration schemes. We solve the equations of motion by an explicit/implicit hierarchical splitting approach, where only the stability sensitive parts are dealt with an implicit scheme, and the remaining parts can be computed explicitly.

• DFG Programme: Research Units
• Subproject of: FOR 5269: Future methods for studying confined gluons in QCD
• International Connection: Ireland
• Cooperation Partner: Professor Dr. Michael Peardon