Effective temperature and scaling laws of polarized quantum vortex bundles

An effective non-equilibrium temperature is defined for (locally) polarized and dense turbulent superfluid vortex bundles, related to the average energy of the excitations (Kelvin waves) of vortex lines. In thequadratic approximation of the excitation energy in terms of the wave amplitude A, a previously known scaling relation between amplitude and wavelength k of Kelvin waves in polarized bundles, namely A proportional to k^(−1/2), follows from the homogeneity of the effective temperature. This result is analogous to that of the well-known equipartition result in equilibrium systems.