Lyapunov Exponent Pairing for a Thermostatted Hard-Sphere Gas under Shear in the Thermodynamic Limit

Details Lyapunov Exponent Pairing for a Thermostatted Hard-Sphere Gas under Shear in the Thermodynamic Limit Lyapunov Exponent Pairing for a Thermostatted Hard-Sphere Gas under Shear in the Thermodynamic Limit

2002-02-05

arxiv.org/abs/nlin/0202016v4

Phys. Rev. E 65, 060102(R) (2002)

Nonlinear Sciences

Chaotic Dynamics

4 pages, to appear in Rapid Comm., Phys. Rev. E

Scientific paper

10.1103/PhysRevE.65.060102

We demonstrate why for a sheared gas of hard spheres, described by the SLLOD equations with an iso-kinetic Gaussian thermostat in between collisions, deviations of the conjugate pairing rule for the Lyapunov spectrum are to be expected, employing a previous result that for a large number of particles $N$, the iso-kinetic Gaussian thermostat is equivalent to a constant friction thermostat, up to $1/\sqrt{N}$ fluctuations. We also show that these deviations are at most of the order of the fourth power in the shear rate.

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