Quantum turbulence and Planckian dissipation

Abstract: The notion of the Planckian dissipation is extended to the system of the Caroli-de Gennes-Matricon discrete energy levels in the vortex core of superconductors and fermionic superfluids. In this extension, the Planck dissipation takes place when the relaxation time $\tau$ is comparable with the quantum Heisenberg time $t_H=\hbar/\Delta E$, where $\Delta E$ is the interlevel distance in the vortex core (the minigap). This type of Planck dissipation has two important physical consequences. First, it determines the regime, when the effect of the axial anomaly becomes important. The anomalous spectral flow of the energy levels along the chiral branch of the Caroli-de Gennes-Matricon states becomes important in the super-Planckian region, i.e. when $\tau <\hbar/\Delta E$. Second, the Planck dissipation separates the laminar flow of the superfluid liquid at $\tau<\hbar/\Delta E$ and the vortex turbulence regime at $\tau>\hbar/\Delta E$.