Quantum Suppression of Alignment in Ultrasmall Grains: Microwave Emission from Spinning Dust will be Negligibly Polarized

The quantization of energy levels in very nanoparticles suppresses dissipative processes that convert grain rotational kinetic energy into heat. For grains small enough to have GHz rotation rates, the suppression of dissipation can be extreme. As a result, alignment of such grains is suppressed. This applies both to alignment of the grain body with its angular momentum J, and to alignment of J with the local magnetic field B_0. If the anomalous microwave emission is rotational emission from spinning grains, it will be negligibly polarized at GHz frequencies, with P < 10^{-6} at frequencies above 10 GHz.