Kolmogorov turbulence, Anderson localization and KAM integrability

摘要

The conditions for emergence of Kolmogorov turbulence, and related weak waveturbulence, in finite size systems are analyzed by analytical methods andnumerical simulations of simple models. The analogy between Kolmogorov energyflow from large to small spacial scales and conductivity in disordered solidstate systems is proposed. It is argued that the Anderson localization can stopsuch an energy flow. The effects of nonlinear wave interactions on such alocalization are analyzed. The results obtained for finite size system modelsshow the existence of an effective chaos border between theKolmogorov-Arnold-Moser (KAM) integrability at weak nonlinearity, when energydoes not flow to small scales, and developed chaos regime emerging above thisborder with the Kolmogorov turbulent energy flow from large to small scales.