Phase-space singularities in atomistic planar diffusive flow

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Abstract
Morriss [Phys. Rev. A 39, 4811 (1989)] recently published a stimulating study of a nonequilibrium Lorentz gas. He measured a multifractal ‘‘spectrum of singularities’’ f(a) describing the ‘‘coarse-grained’’ phase space-representation of a time-reversible, two-body, space- and time-periodic shear flow. The measured function f(a) is the ‘‘Hausdorff dimension’’ of attractor singularities whose local bin integrals vary as the ath power of the bin length. Morriss found a spectrum of singularities f(a) very different from those familiar to nonlinear dynamical systems theory. Here we consider a closely related, but simpler, two-body time-reversible atomistic system. It is also a Lorentz-gas problem, a nonequilibrium diffusive flow, periodic in space but stationary in time. This system appears to be both mixing and ergodic, even far from equilibrium. We use the Chhabra-Jensen technique to show that the phase-space singularity spectrum f(a) for this nonequilibrium flow more closely resembles those of dynamical systems theory.