Analysis of quantum 1/f effects in frequency standards

There is a fundamental limitation of the stability of frequency standards, caused by the quantum 1/f effect. This effect represents a quantum fluctuation of the physical currents, scattering cross sections and process rates, caused by the reaction of Bremsstrahlung on the charged particles which have emitted it. It is the only known quantum effect which is inversely proportional to Planck´s constant, and which is therefore important in the limit of low, rather than high frequencies. In frequency standards the rate of change of the dipolar moment of the oscillating material system suffers a discontinuity every time an oscillation quantum is absorbed in the loss process. This causes the emission of elf bremsstrahlung and therefore quantum 1/f fluctuations in the loss rate, which translate into 1/fQ⁴ frequency fluctuations