Classical and quantum dynamics of electrons in open equilateral triangular billiards

Experimental and theoretical studies of the electron dynamics in open equilateral triangular billiards are presented. We focus on the question to what extent classical mechanics can be used to model electron transport in comparison to a fully quantum-mechanical treatment. The classical simulations of the magnetoresistance, which are based on a billiard-ball model, agree in great detail with the temperature averaged, gross features of the measured data. The frequency of experimentally observed conductance fluctuations can be related to a simple closed electron orbit, which, in turn, is shown to be particularly important for classical electron dynamics. The magnetoresistance calculated quantum mechanically shows, in addition to the (classical) gross features, also quasiperiodic conductance fluctuations in the same frequency range as experimentally observed. We address the effect of the distortion of the classical trajectories induced by the magnetic field on the frequency of the conductance fluctuations. This effect appears to be less important in small samples. In order to also visually compare the classical and quantum-mechanical pictures of electron transport, plots of the particle density inside the billiard are presented, which were obtained with both classical and quantum-mechanical methods. The resemblance is weak at low-magnetic fields, while at high fields strikingly similar images are obtained with the two techniques.