The Lyapunov spectrum of the many-dimensional dilute random Lorentz gas

Abstract

For a better understanding of the chaotic behavior of systems of many moving particles it is useful to look at other systems with many degrees of freedom. An interesting example is the high-dimensional Lorentz gas, which, just like a system of moving hard spheres, may be interpreted as a dynamical system consisting of a point particle in a high-dimensional phase space, moving among fixed scatterers. In this paper, we calculate the full spectrum of Lyapunov exponents for the dilute random Lorentz gas in an arbitrary number of dimensions. We find that the spectrum becomes flatter with increasing dimensionality. Furthermore, for fixed collision frequency the separation between the largest Lyapunov exponent and the second largest one increases logarithmically with dimensionality, whereas the separations between Lyapunov exponents of given indices not involving the largest one, go to fixed limits.

8 pages, revtex, 6 figures, submitted to Physical Review E

References in corpus (2)

• Goldstone modes in Lyapunov spectra of hard sphere systems
• Front propagation techniques to calculate the largest Lyapunov exponent of dilute hard disk gases

Cited by in corpus (6)

• Lyapunov instabilities in lattices of interacting classical spins at infinite temperature
• The Kolmogorov-Sinai entropy for dilute systems of hard particles in equilibrium
• Lyapunov spectra of billiards with cylindrical scatterers: comparison with many-particle systems
• Thermodynamic formalism for the Lorentz gas with open boundaries in $d$ dimensions
• Radius of curvature approach to the Kolmogorov-Sinai entropy of dilute hard particles in equilibrium
• Equivalence of kinetic-theory and random-matrix approaches to Lyapunov spectra of hard-sphere systems