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arXiv · 2310.13696

Lyapunov vectors and excited energy levels of the directed polymer in random media

Enrique Rodriguez·Juan M. Lopez
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Abstract

The scaling behavior of the excited energy levels of the directed polymer in random media is analyzed numerically. We find that the spatial correlations of polymer energies scale as $\sim k^{-\delta}$ for small enough wavenumbers $k$ with a nontrivial exponent $\delta \approx 1.3$. The equivalence between the stochastic-field equation that describes the partition function of the directed polymer and that governing the time evolution of infinitesimal perturbations in space-time chaos is exploited to connect this exponent $\delta$ with the spatial correlations of Lyapunov vectors reported in the literature. The relevance of our results for other problems involving optimization in random systems is discussed.

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Enrique Rodriguez, Juan M. Lopez. 2023-09-19. Lyapunov vectors and excited energy levels of the directed polymer in random media. https://arxiv.org/abs/2310.13696

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