Mori-Zwanzig formalism as a practical computational tool.
An operational procedure is presented to compute explicitly the different terms in the generalized Langevin equation (GLE) for a few relevant variables obtained within Mori-Zwanzig formalism. The procedure amounts to introducing an artificial controlled parameter which can be tuned in such a way that the so-called projected dynamics becomes explicit and the GLE reduces to a Markovian equation. The projected dynamics can be realised in practice by introducing constraints, and it is shown that the Green-Kubo formulae computed with these dynamics do not suffer from the plateau problem. The methodology is illustrated in the example of star polymer molecules in a melt using their center of mass as relevant variables. Through this example, we show that not only the effective potentials, but also the friction forces and the noise play a very important role in the dynamics.
Departamento de Física Fundamental, Universidad Nacional de Educación a Distancia, Aptdo. 60141, E-28080 Madrid, Spain.
Carmen
C
Hijón
Pep
P
Español
Eric
E
Vanden-Eijnden
Rafael
R
Delgado-Buscalioni