ABSTRACT
Abstract. To check the reliability of random matrix theory and semiclassical theory to predict the transport properties in quantum cavities having regular or chaotic underlying classical dynamics, we compute the conductance numerically using the tight-binding model. The average conductance develops a Lorentzianshaped dip near zero magnetic field in accordance with the prediction provided that the dynamics is fully chaotic. The weak localization effect is absent if the dynamics is regular or merely partially chaotic. The amplitude of conductance fluctuations in regular cavities is revealed to be about twice as large as that in chaotic cavities. These observations caution against the application of the analytical theories for nonchaotic dynamics. We also demonstrate that the statistics of the nearest-neighbor energy level separation can be inferred from the conductance fluctuations. 1
1. Introduction
There are a large number of experimental [1,2] and theoretical [3-6] investigations in the last decade on the conductance of microcavities prepared from a two-dimensional electron gas having dimensions less than the elastic mean free path of the electrons but far greater than the Fermi wavelength XF. The cavities are, at the same time, smaller than the phase coherence length of the electrons. The transport characteristics, therefore, significantly reflect the classical dynamics in the cavities in spite of the fact that the conductance is fully determined by quantum mechanics. These microfabricated devices enable us to alter the underlying classical dynamics from being regular to being chaotic by varying the cavity geometry. They are hence suitable to investigate the correspondence between the classical dynamics and the quantum transport properties.
