Relation between stable orbits and quantum transmission resonance in ballistic cavities

Classical and quantum-mechanical transport properties in chaotic cavities are investigated to establish a link between them. Because of the stickiness at the boundary between stochastic seas and islands of regular orbits in phase space, classical trajectories spend a long time in the vicinity of a few regular orbits. The trapping results in an exclusive excitation of these stable orbits even when the cavity is terminated by classical leads. The wave-function pattern at quantum transmission resonances is found to be identical with one of the stable orbits. The correspondence implies that the transmission resonance takes place when the stable orbit satisfies Bohr and Sommerfeld's quantization rule, and hence explains why conductance fluctuations in ballistic cavities contain only several frequency components.