Lyapunov exponents and transport in Self-Organized Criticality
Abstract
We discuss the role played by the Lyapunov exponents in the dynamics of the Zhang's model of Self-Organized Criticality. We show that a wide part in the spectrum (slowest modes) is associated to energy transport in the lattice. We give in particular bounds on the first negative Lyapunov exponents in terms of the energy flux dissipated at the boundaries per unit time. We then establish an explicit formula for the transport modes, that appear as diffusion modes in a landscape where the metric is given by the density of active sites. We use a finite size scaling ansatz for the Lyapunov spectrum and relate the scaling exponent to the scaling of quantities like avalanche size, duration, density of active site, etc ...Keywords
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