We have developed a method for calculation of quantum fluctuation effects, in particular, of the uncertainty zone developing at the potential curvature sign inversion, for a damped harmonic oscillator with arbitrary time dependence of frequency and for arbitrary temperature, within the Caldeira-Leggett model. The method has been applied to the calculation of the gray zone width ΔIx of Josephson-junction balanced comparators. The calculated temperature dependence of ΔIx in the range 1.5 to 4.2 K is in virtually perfect agreement with experimental data for Nb-trilayer comparators with critical current densities of 1.0 and 5.5kA/cm2, without any fitting parameters.

• Received 15 July 2002

DOI:https://doi.org/10.1103/PhysRevLett.89.217004