2023/09/19 by Rodriguez, Enrique, Lopez, Juan M.
#FOS: Physical sciences #Soft Condensed Matter (cond-mat.soft) #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.2310.13696
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 ∼ k-δ for small enough wavenumbers 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 Lyapunov vectors reported in the literature. The relevance of our results for other problems involving optimization in random systems is discussed.