Inertial range and the Kolmogorov spectrum of quantum turbulence

Quantum turbulence is numerically studied by solving the Gross-Pitaevskii equation. By introducing both energy dissipation at small scales and energy injection at large scales, we succeed in obtaining steady turbulence sustained by a balance between energy injection and energy dissipation. The energy spectrum in the inertial range takes the form of the Kolmogorov spectrum and the energy flux is consistent with the energy dissipation rate at small scales. These results reveal the proper-ties of quantum turbulence in the inertial range, allowing us to propose a prototype of turbulence much simpler than conventional classical turbulence.