Shearing a fermionic gas and quantized friction

The frictional forces in sheared fermionic gas are investigated. The gas is sheared by two sliding surfaces. Except for a small imperfection (bulge) on one of them, the surfaces are totally smooth. We show that when the bulge is extremely small, and the gas is also confined in the lateral dimension, the frictional force (F) is quantized. That is, F≤μ_Fv, where v is the sliding velocity with respect to the lubricant gas, μ_F≡ 2mn_c²h is the friction coefficient, h is the Planck constant and m is an integer. It is also shown that the coefficient n _c depends only on the bulge's properties (it does not depend on either the gas properties or the sliding velocity).