Quantum turbulence and Planckian dissipation

TL;DR

This paper extends the concept of Planckian dissipation to vortex core energy levels in superconductors and superfluids, revealing its role in quantum turbulence and axial anomaly effects.

Contribution

It introduces a new framework linking Planckian dissipation to vortex core states and quantum turbulence in superconductors and superfluids.

Findings

Planck dissipation occurs when relaxation time matches quantum Heisenberg time.

It influences the axial anomaly and spectral flow in vortex core states.

Dissipation separates laminar flow from vortex turbulence.

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 $\tau>\hbar/\Delta E$.