Transient Oscillation of Currents in Quantum Hall Effect of Bloch Electrons

TL;DR

This paper investigates the transient behavior of currents in the quantum Hall effect of Bloch electrons, revealing oscillations caused by quantum fluctuations that decay over time after an abrupt electric field application.

Contribution

It provides a theoretical analysis of the time-dependent oscillations of Hall and longitudinal currents in a quantum Hall system with a periodic potential.

Findings

Currents oscillate with very high frequencies due to quantum fluctuations.

Oscillations decay as 1/t over time.

Transient oscillations vanish after initial disturbance.

Abstract

We consider the quantum Hall effect of two-dimensional electrons with a periodic potential and study the time dependence of the Hall and longitudinal currents when the electric field is applied abruptly. We find that the currents oscillate in time with very large frequencies because of quantum fluctuation and the oscillations eventually vanish, for their amplitudes decay as 1/t.