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The structure of Lyapunov spectra for many particle systems with a randominteraction between the particles is discussed. The dynamics of the tangentspace is expressed as a master equation, which leads to a formula that connectsthe positive Lyapunov exponents and the time correlations of the particleinteraction matrix. Applying this formula to one and two dimensional models weinvestigate the stepwise structure of the Lyapunov spectra, which appear in theregion of small positive Lyapunov exponents. Long range interactions lead to aclear separation of the Lyapunov spectra into a part exhibiting stepwisestructure and a part changing smoothly. The part of the Lyapunov spectrumcontaining the stepwise structure is clearly distinguished by a wave likestructure in the eigenstates of the particle interaction matrix. The twodimensional model has the same step widths as found numerically in adeterministic chaotic system of many hard disks.Comment: 15 pages, 6 figure

Stepwise structure of Lyapunov spectra for many-particle systems using a random matrix dynamics