Pairing of Lyapunov exponents for a hard-sphere gas under shear in the thermodynamic limit.
We consider a dilute gas of hard spheres under shear. We use one of the predominant models to study this system, namely, the so-called SLLOD equations of motion, with an isokinetic Gaussian thermostat in between collisions, to get a stationary total peculiar kinetic energy. Based on the previously obtained result that in the nonequilibrium steady state and in the case the number of particles N becomes large, the coefficient of dynamical friction representing the isokinetic Gaussian thermostat for the SLLOD dynamics fluctuates with 1/sqrt[N] fluctuations around a fixed value, we show on analytical grounds that for a hard sphere gas at small shear rate and with a large number of spheres, the conjugate pairing of the Lyapunov exponents is expected to be violated at the fourth power of the constant shear rate in the bulk.
Panja
Debabrata
D
Instituut Lorentz, Universiteit Leiden, Postbus 9506, 2300 RA Leiden, The Netherlands.
Van Zon
Ramses
R