1:30 pm MCP 201
Renormalization and universality in wave turburlance.
The Gross-Pitaevskii (GP) model, also known as the nonlinear Schrodinger equation, is arguably the most universal model in classical and quantum physics, describing spectrally narrow or long-wavelength distributions of interacting waves or particles. Modern applications --- from oceanic and atmospheric flows to photonics and cold atoms --- predominantly involve states that are far from equilibrium, culminating in the regime of fully developed turbulence. To date, a consistent theoretical description of such states has only existed for weakly interacting quasiparticles. Here we present a theory of strong turbulence in the two-dimensional N-component Gross-Pitaevskii model for both repulsive and attractive interactions, corresponding to the defocusing and focusing cases, respectively. In the focusing case, we show that attraction is enhanced by multi-wave effects, leading to a critical-balance state independent of the pumping level. In the defocusing case, repulsion is suppressed by collective effects, giving rise to another type of universality in strong turbulence --- independence from the bare coupling constant. The theory is confirmed by analytical results in the many-component limit and by direct numerical simulations of the single-component GP model.