Viscosity of Quantum Hall Fluids

TL;DR

This paper calculates the non-dissipative viscosity of quantum Hall fluids on two-dimensional tori, revealing that it is quantized and proportional to the magnetic flux, linking geometric properties to physical responses.

Contribution

It provides an explicit computation of the viscosity for quantum Hall fluids on tori, demonstrating its quantization and dependence on magnetic flux.

Findings

Viscosity is non-dissipative and related to adiabatic curvature.

Average viscosity on a torus is quantized.

Viscosity is proportional to total magnetic flux.

Abstract

The viscosity of quantum fluids with an energy gap at zero temperature is non-dissipative and is related to the adiabatic curvature on the space of flat background metrics (which plays the role of the parameter space). For a quantum Hall fluid on two dimensional tori this viscosity is computed. In this case the average viscosity is quantized and is proportional to the total magnetic flux through the torus.