Lyapunov vectors and excited energy states of the directed polymer in random media Articles uri icon

authors

  • RODRIGUEZ FERNANDEZ, ENRIQUE
  • Lopez, Juan M.

publication date

  • January 2024

start page

  • L012102

issue

  • 1

volume

  • 109

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

subjects

  • Physics