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

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