Inner Nonlinear Waves and Inelastic Light Scattering of Fractional Quantum Hall States as Evidence of the Gravitational Anomaly

TL;DR

This paper develops a quantum hydrodynamics framework for inner waves in fractional quantum Hall states, linking inelastic light scattering to gravitational anomalies and providing a model-independent formula for optical absorption.

Contribution

It introduces a novel quantum hydrodynamics approach for fractional quantum Hall states and connects gravitational anomalies to observable optical properties.

Findings

Inelastic light scattering is caused solely by gravitational anomalies.

Derived a formula for optical absorption depending only on measurable static structure factor.

The formula is independent of specific interaction potentials.

Abstract

We develop the quantum hydrodynamics of inner waves in the bulk of fractional quantum Hall states. We show that the inelastic light scattering by inner waves is a sole effect of the gravitational anomaly. We obtain the formula for the oscillator-strength or mean energy of optical absorption expressed solely in terms of an independently measurable static structure factor. The formula does not explicitly depend on a model interaction potential.