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We study effects of the oft-neglected cubic Dresselhaus spin-orbit coupling(i.e., $\propto p^3$) in GaAs/AlGaAs quantum dots. Using a semiclassicalbilliard model, we estimate the magnitude of the spin-orbit induced avoidedcrossings in a closed quantum dot in a Zeeman field. Using these results,together with previous analyses based on random matrix theory, we calculatecorresponding effects on the conductance through an open quantum dot. Combiningour results with an experiment on conductance through an 8 um^2 quantum dot [DM Zumbuhl et al., Phys. Rev. B 72, 081305 (2005)] suggests that 1) the GaAsDresselhaus coupling constant, $\gamma$, is approximately 9 eVA^3,significantly less than the commonly cited value of 27.5 eVA^3 and 2) themajority of the spin-flip component of spin-orbit coupling can come from thecubic Dresselhaus term.Comment: 4 pages plus supplementary tabl

Cubic Dresselhaus Spin-Orbit Coupling in 2D Electron Quantum Dots