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Abstract: Two deterministic models for Brownian motion are investigated by means ofnumerical simulations and kinetic theory arguments. The first model consists ofa heavy hard disk immersed in a rarefied gas of smaller and lighter hard disksacting as a thermal bath. The second is the same except for the shape of theparticles, which is now square. The basic difference of these two systems liesin the interaction: hard core elastic collisions make the dynamics of the diskschaotic whereas that of squares is not. Remarkably, this difference is notreflected in the transport properties of the two systems: simulations show thatthe diffusion coefficients, velocity correlations and response functions of theheavy impurity are in agreement with kinetic theory for both the chaotic andthe non-chaotic model. The relaxation to equilibrium, however, is verysensitive to the kind of interaction. These observations are used to reconsiderand discuss some issues connected to chaos, statistical mechanics anddiffusion.



Author: Fabio Cecconi, Massimo Cencini, Angelo Vulpiani

Source: https://arxiv.org/



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