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Volume 144, 2010
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Mori–Zwanzig formalism as a practical computational tool

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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.

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Article information

05 Feb 2009
24 Feb 2009
First published
12 Aug 2009

Faraday Discuss., 2010,144, 301-322
Article type

Mori–Zwanzig formalism as a practical computational tool

C. Hijón, P. Español, E. Vanden-Eijnden and R. Delgado-Buscalioni, Faraday Discuss., 2010, 144, 301
DOI: 10.1039/B902479B

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