On the Validity of Stochastic Rate Equations in Finite Systems with Finite Strength Interactions
CALIFORNIA UNIV SAN DIEGO LA JOLLA DEPT OF CHEMISTRY
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Starting with the Hamiltonian for a linear harmonic chain of 2N particles of mass m and one of mass M the authors have carried out numerical calculations for the momentum autocorrelation function of the mass defect particle for chains with finite number N of mass points and for non-zero values of the mass ratio mu is identically mM. These results have been compared with the well known exponential relaxation of the momentum autocorrelation function which is found to be the rigorous result when passing to the thermodynamic and weak coupling limit. In these limits the dynamics of the mass defect particle is exactly described by a Fokker-Planck equation, i.e. a stochastic equation of motion. The authors have shown that to an excellent approximation an exponential relaxation of the momentum autocorrelation function is obtained for mass ratios as high as mu 0.1 and for chains with only fifty particles. Thus, for the harmonic chain considered here, the stochastic equations of motion can be applied to a very good approximation far outside the usually imposed thermodynamic and weak coupling limits.
- Physical Chemistry