From integrable to chaotic systems: Universal local statistics of Lyapunov exponents

@article{Akemann2018FromIT,
title={From integrable to chaotic systems: Universal local statistics of Lyapunov exponents},
author={G. Akemann and Z. Burda and M. Kieburg},
journal={EPL},
year={2018},
volume={126},
pages={40001}
}
• Published 2018
• Mathematics, Physics
• EPL
Systems where time evolution follows a multiplicative process are ubiquitous in physics. We study a toy model for such systems where each time step is given by multiplication with an independent random $N\times N$ matrix with complex Gaussian elements, the complex Ginibre ensemble. This model allows to explicitly compute the Lyapunov exponents and local correlations amongst them, when the number of factors $M$ becomes large. While the smallest eigenvalues always remain deterministic, which is… Expand

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