TY - BOOK

T1 - Visualization of Oscillatory Electron Dynamics on the Surface of Liquid Helium

AU - Siddiq, Hala

PY - 2023

Y1 - 2023

N2 - We investigate time traces of the currents generated by the motion of electronson the surface of liquid helium that are placed in a perpendicular magnetic fieldand exposed to microwave radiation. Nonlinear dynamics methods are utilized toexplore the characteristic features of the current oscillations from five electrodesat different electron densities and pressing voltages. The wavelet phase coherenceand phase shift are calculated to obtain the coherence relationships between thecurrents in the five electrodes, and the direction of motion of electrons inside thecell, as functions of the pressing voltage. These classical methods reveal that theelectron motion is oscillatory with varying frequency and with a constant frequency modulation. Higher harmonics due to nonlinearity arise at higher frequencies where the the resonance condition for inter-subband transition is satisfied at a pressing voltage of 4.20 V for low electron density. Our approach provides a platform for investigating these phenomena analytically. We show that slow helium gravity waves modulate the electronic oscillatory behaviour and illustrate that the model in fact produces 3D dynamics. Motion of electrons on the surface of liquid helium is shown to be a paradigmatic example of a chronotaxic system, i.e. a system that undergoes continuous perturbation and is nonetheless capable of maintaining its stability.

AB - We investigate time traces of the currents generated by the motion of electronson the surface of liquid helium that are placed in a perpendicular magnetic fieldand exposed to microwave radiation. Nonlinear dynamics methods are utilized toexplore the characteristic features of the current oscillations from five electrodesat different electron densities and pressing voltages. The wavelet phase coherenceand phase shift are calculated to obtain the coherence relationships between thecurrents in the five electrodes, and the direction of motion of electrons inside thecell, as functions of the pressing voltage. These classical methods reveal that theelectron motion is oscillatory with varying frequency and with a constant frequency modulation. Higher harmonics due to nonlinearity arise at higher frequencies where the the resonance condition for inter-subband transition is satisfied at a pressing voltage of 4.20 V for low electron density. Our approach provides a platform for investigating these phenomena analytically. We show that slow helium gravity waves modulate the electronic oscillatory behaviour and illustrate that the model in fact produces 3D dynamics. Motion of electrons on the surface of liquid helium is shown to be a paradigmatic example of a chronotaxic system, i.e. a system that undergoes continuous perturbation and is nonetheless capable of maintaining its stability.

M3 - Doctoral Thesis

PB - Lancaster University

ER -