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arXiv · 1012.3449

NVU dynamics. II. Comparing to four other dynamics

Trond S. Ingebrigtsen·Søren Toxvaerd·Thomas B. Schrøder·Jeppe C. Dyre
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Abstract

In the companion paper [Ingebrigtsen et al., arXiv:1012.3447] an algorithm was developed for tracing out a geodesic curve on the constant-potential-energy hypersurface. Here simulations of this NVU dynamics are compared to results for four other dynamics, both deterministic and stochastic. First, NVU dynamics is compared to the standard energy-conserving Newtonian NVE dynamics by simulations of the Kob-Andersen binary Lennard-Jones liquid, its WCA version (i.e., with cut-off's at the pair potential minima), and the Gaussian Lennard-Jones liquid. We find identical results for all quantities probed: radial distribution functions, incoherent intermediate scattering functions, and mean-square displacement as function of time. Arguments are then presented for the equivalence of NVU and NVE dynamics in the thermodynamic limit; in particular to leading order in 1/N these two dynamics give identical time-autocorrelation functions. In the final section NVU dynamics is compared to Monte Carlo dynamics, to a diffusive dynamics of small-step random walks on the constant-potential-energy hypersurface, and to Nose-Hoover NVT dynamics. If time is scaled for the two stochastic dynamics to make their single-particle diffusion constants identical to those of NVE dynamics, the simulations show that all five dynamics are equivalent at low temperatures except at short times.

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Trond S. Ingebrigtsen, Søren Toxvaerd, Thomas B. Schrøder, Jeppe C. Dyre. 2011-08-06. NVU dynamics. II. Comparing to four other dynamics. https://doi.org/10.1063/1.3623586

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