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

Rodríguez-Fernández, Enrique; López, Juan M · Phys Rev E · 2024

basic_science · Level V

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Abstract

The scaling behavior of the excited energy states of the directed polymer in random media is analyzed numerically. We find that the spatial correlations of polymer energies scale as ∼k^{-δ} for small enough wave numbers k with a nontrivial exponent δ≈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 δ with the spatial correlations of the Lyapunov vectors reported in the literature. The relevance of our results for other problems involving optimization in random systems is discussed.