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 $\sim k^{-\delta }$ for small enough wave numbers $k$ 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 the Lyapunov vectors reported in the literature. The relevance of our results for other problems involving optimization in random systems is discussed.

Close

PrevNext

View figure in article

• Nonequilibrium statistical mechanics
• Spatiotemporal chaos
• Chaotic systems
• Disordered systems
• Nonequilibrium systems
• Surface growth
• Chaos & nonlinear dynamics
• Critical phenomena
• Finite-size scaling
• Kardar–Parisi–Zhang equation
• Monte Carlo methods
• Scaling methods