Numerical integration of the extended variable generalized Langevin equation with a positive Prony representable memory kernel

摘要

Generalized Langevin dynamics (GLD) arise in the modeling of a number ofsystems, ranging from structured fluids that exhibit a viscoelastic mechanicalresponse, to biological systems, and other media that exhibit anomalousdiffusive phenomena. Molecular dynamics (MD) simulations that include GLD inconjunction with external and/or pairwise forces require the development ofnumerical integrators that are efficient, stable, and have known convergenceproperties. In this article, we derive a family of extended variableintegrators for the Generalized Langevin equation (GLE) with a positive Pronyseries memory kernel. Using stability and error analysis, we identify asuperlative choice of parameters and implement the corresponding numericalalgorithm in the LAMMPS MD software package. Salient features of the algorithminclude exact conservation of the first and second moments of the equilibriumvelocity distribution in some important cases, stable behavior in the limit ofconventional Langevin dynamics, and the use of a convolution-free formalismthat obviates the need for explicit storage of the time history of particlevelocities. Capability is demonstrated with respect to accuracy in numerouscanonical examples, stability in certain limits, and an exemplary applicationin which the effect of a harmonic confining potential is mapped onto a memorykernel.