Friction tensor for a pair of Brownian particles: Spurious finite-size effects and molecular dynamics estimates

Journal Article · Wed Oct 01 04:00:00 EDT 1997 · Journal of Statistical Physics

DOI:https://doi.org/10.1007/BF02770768· OSTI ID:569814

Bocquet, L; Hansen, J P; Piasecki, J ^[1]

---

1. Ecole Normale Superieure de Lyon (France)

In this work, we show that in any finite system, the binary friction tenser for two Brownian particles cannot be directly estimated from an evaluation of the microscopic Green Kubo formula, involving the time integral of force-force autocorrelation functions. This pitfall is associated with a subtle inversion of the thermodynamic and long-time limits and leads to spurious results for the estimates of the friction matrix based on molecular dynamics simulations. Starting from a careful analysis of the coupled Langevin equations for two interacting Brownian particles, we derive a method to circumvent these effects and extract the binary friction tenser from the correlation function matrix of the instantaneous forces exerted by the bath particles on the fixed Brownian particles, and from the relaxation of the total momentum of the bath in a finite system. The general methodology is applied to the case of two hard or soft Brownian spheres in a bath of light particles. Numerical estimates of the relevant correlation functions and of the resulting self and mutual components of the matrix of friction tensors are obtained by molecular dynamics simulations for various spacings between the Brownian particles.

• Sponsoring Organization: USDOE
• OSTI ID: 569814
• Journal Information: Journal of Statistical Physics, Journal Name: Journal of Statistical Physics Journal Issue: 1-2 Vol. 89; ISSN JSTPBS; ISSN 0022-4715
• Country of Publication: United States
• Language: English

Related Subjects

40 CHEMISTRY
66 PHYSICS
BROWNIAN MOVEMENT
CORRELATION FUNCTIONS
FRICTION
MOLECULAR DYNAMICS METHOD