Chaotic Properties of Dilute Two and Three Dimensional Random Lorentz Gases II: Open Systems

Abstract

We calculate the spectrum of Lyapunov exponents for a point particle moving in a random array of fixed hard disk or hard sphere scatterers, i.e. the disordered Lorentz gas, in a generic nonequilibrium situation. In a large system which is finite in at least some directions, and with absorbing boundary conditions, the moving particle escapes the system with probability one. However, there is a set of zero Lebesgue measure of initial phase points for the moving particle, such that escape never occurs. Typically, this set of points forms a fractal repeller, and the Lyapunov spectrum is calculated here for trajectories on this repeller. For this calculation, we need the solution of the recently introduced extended Boltzmann equation for the nonequilibrium distribution of the radius of curvature matrix and the solution of the standard Boltzmann equation. The escape-rate formalism then gives an explicit result for the Kolmogorov Sinai entropy on the repeller.

submitted to Phys Rev E

References in corpus (4)

• Largest Lyapunov Exponent for Many Particle Systems at Low Densities
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• Chaotic Properties of Dilute Two and Three Dimensional Random Lorentz Gases I: Equilibrium Systems
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Cited by in corpus (12)

• Hamiltonian dynamics, nanosystems, and nonequilibrium statistical mechanics
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• Viscosity in the escape-rate formalism
• When do tracer particles dominate the Lyapunov spectrum?
• Front propagation techniques to calculate the largest Lyapunov exponent of dilute hard disk gases
• Thermodynamic formalism for field driven Lorentz gases
• Thermodynamic formalism for the Lorentz gas with open boundaries in $d$ dimensions
• Systematic Density Expansion of the Lyapunov Exponents for a Two-dimensional Random Lorentz Gas
• Stable regimes for hard disks in a channel with twisting walls
• Efficient algorithms for general periodic Lorentz gases in two and three dimensions
• Lyapunov exponent for a gas of soft scatterers
• Long-time-tail Effects on Lyapunov Exponents of a Random, Two-dimensional Field-driven Lorentz Gas