  A thermal model of kinetic friction is assigned to a classical loaded
particle moving on a fluctuating smooth surface. A sinusoidal wave resembles
surface fluctuations with a relaxation time. The Hamiltonian is approximated to
the mean energy of the wave describing a system of Harmonic oscillators. The
quantization of amplitudes yields in terms of annihilation and creation
operators multiplied by a quantum phase. Further, we consider acoustic
dispersion relation and evaluate the friction coefficient from the force
autocorrelation function. While the sliding particle remains classical
describing a nano-particle or a tip with negligible quantum effects like
tunneling or delocalization in the wave function, the quantized model of the
surface fluctuations results in the temperature dependence of the kinetic
friction coefficient. It follows an asymptotic value for higher temperatures
and supperslipperiness at low temperatures.
