  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.
