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Karhunen-Lo`eve Decomposition of Extensive Chaos

Scott M. Zoldi·Henry S. Greenside
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Abstract

We show that the number of KLD (Karhunen-Lo`eve decomposition) modes D_KLD(f) needed to capture a fraction f of the total variance of an extensively chaotic state scales extensively with subsystem volume V. This allows a correlation length xi_KLD(f) to be defined that is easily calculated from spatially localized data. We show that xi_KLD(f) has a parametric dependence similar to that of the dimension correlation length and demonstrate that this length can be used to characterize high-dimensional inhomogeneous spatiotemporal chaos.

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Scott M. Zoldi, Henry S. Greenside. 1996-10-02. Karhunen-Lo`eve Decomposition of Extensive Chaos. https://doi.org/10.1103/physrevlett.78.1687

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